UNRESTED and unshowered, I arrived at Luton Airport, in suburban London, around 5 a.m., and did not expect my situation to improve. I’d been up all night, wandering around London with friends, and now I was about to fly to Morocco on an airline whose reputation for rock-bottom prices was surpassed only by its reputation for rock-bottom service. Bleary-eyed, I slapped my passport on the check-in counter, picked up the boarding pass (no assigned seating, of course), and began the long, long march to my gate.

Normally, I would have shrugged off the looming discomfort as I did the attendant’s warning about my overweight baggage. But I was halfway through a weeklong jaunt around Europe, traveling solely via low-cost carriers, the budget airlines that have multiplied across the Continent like unnecessary E.U. regulations, and the perpetual motion was getting to me. Where had I just been? Where was I going? I wasn’t really sure anymore — all I knew was that getting there wouldn’t cost much more than my sanity.

Every country or region has at least one budget airline: easyJet and RyanAir, the pioneers in this industry, operate out of the Britain and Ireland, while Air Berlin and HLX ferry the shallow-pocketed in and out of Germany. Spain has Vueling, Scandinavia has Sterling, and Italy has a host of tiny carriers that focus on random, disparate cities — Evolavia, for example, flies between Ancona, Paris and Moscow.

What unites these small airlines is a devotion to cheap fares. Flights routinely are less than 20 euros (about $27 at $1.36 to the euro), and can even drop to the low, low price of ... zero. How can the airlines afford that? By cutting out frills and tacking on fees. Fuel surcharges, airport taxes, excess-baggage fees and the ever-popular miscellaneous charges help make up for the seemingly unprofitable ticket prices.

Despite this sneakiness, these airlines remain the best way to bounce around the increasingly borderless superstate known as Europe — faster than railroads, more comfortable than a bus (if you’re lucky), and far cheaper than the major carriers.

This winter, I set out to test the network. The plan: seven flights in seven days, mixing established and off-the-beaten-path destinations, staying in modest hotels and never taking the same airline twice. Along the way, I would even try to enjoy myself wherever I landed.

At first, mapping out a route late last November drove me crazy. Not all budget airlines fly every route every day, and plugging schedules into Web sites took hours. Then I discovered Flylc.com, a booking engine that streamlines the process. Its page shows three columns: the first contains a list of every airport in Europe; click one and the second column displays every destination you can reach from there, while the third shows which airlines fly that route. One more click brings up a timetable showing every flight from, say, Dublin to Bratislava on SkyEurope. Neat!

Soon I had a drawn a viable route around Europe. From Geneva — a central location served by many budget airlines — I’d fly to Prague, then to Copenhagen, London, Fez (Morocco is around Europe, right?), Paris and Budapest, and back to Geneva. At each stop, I’d have a day, more or less, to get oriented before rushing off to the next far-flung city. Lather, rinse, repeat.

And so, early one January Monday in Geneva, I checked into Flybaboo Flight 75. Founded in 2003, the improbably named airline generally ferries passengers to warmer climes — the French Riviera, Ibiza, Sardinia — but for a mere 10 Swiss francs (about $8 at $1.24 Swiss francs to the U.S. dollar, but the equivalent of $59 with taxes), it also goes to Prague. As I walked to the farthest reaches of the airport, where Flybaboo’s gates lay, I wondered what I was getting into.

Then I arrived at the Flybaboo lounge — the slickest non-business-class waiting area I’d ever seen. Men in good suits sat on the red-leather banquettes, checking e-mail on complimentary iMacs. I picked up a copy of Baboo Time, a smart, stylish magazine, and read an interview with Dita Von Teese. I was in no hurry to board, because I worried that things could only get worse.

They got better. The plane was a cute twin-prop Dash 8-300, and as we sat shivering on the runway, waiting for the wings to be de-iced, the sole flight attendant — a young guy whose nice gray wool trousers and black V-neck sweater were accented by a red tie and a red nylon belt — kindly handed out blankets. A few minutes later, we took off, cruising up through the darkness to the clear sky, where the gray quilt of clouds stretched out before us, punctured by the peaks of the Jura Mountains, glowing in the first light of dawn. I gazed out the window till breakfast arrived — strong coffee and airy, just-sweet muffins — then snuggled under my blanket till we touched down, on time, in Prague.

A bus and a subway took me to the heart of Prague’s old town, where after a few wrong turns I arrived at my hotel, the Jerome House. I had a big, clean room, and I made the most of my 24 hours in the Czech capital, wandering the ancient streets and bridges, eating and drinking with friends of friends, and popping into the Kafka Museum for a peek into the life of the writer whose work is all about disorientation.

Too soon, it was back to the airport for Sterling Flight 564 to Copenhagen (7 euros, or 31 euros with taxes and fees). After Flybaboo, Sterling was a disappointment: service was efficient but impersonal, and the flight attendants wore brown pantsuits with tight brown gloves — the corporate dominatrix look. Worse, the Boeing 737-800 was filthy. The dark blue seat fabric hid ground-in grime, fingerprints smeared the windows, and the unmistakable smell of body odor lingered in the stale air. A flavorless chicken sandwich and a Diet Coke cost 8 euros. Luckily, the in-flight magazine provided distraction with an article on eco-friendly Danish fashion and an interview with Lars von Trier.

Less than an hour after we touched down, I arrived by speedy train at Copenhagen’s main station. Climbing up from the platform, I spotted an ad for my hotel that included directions. I turned right, then left, then right again — and promptly found myself nowhere near the Cab Inn. Instead, I was circling around the dark gates of Tivoli, the grand amusement park smack in the middle of downtown. The ad’s directions had seemed so clear — but where was I going?

Though the sky looked ready to pour at any minute, I pulled my MacBook from my messenger bag, found a public Wi-Fi signal and loaded the Cab Inn Web site: The hotel had moved from one side of Tivoli to the other; the train-station ad had not been updated. Fifteen minutes later I was in my room, designed to look like a ship’s cabin.

That evening, I reunited with Egil, a friend since childhood, and along with his girlfriend and his brother, we ate at Det Lille Apotek, which claims to be Copenhagen’s oldest restaurant. In the quaint little tavern, where Egil’s grandfather, the painter Asger Jorn, used to hang out, we reminisced over old times and devoured roast beef, gravy and way too many potatoes. I’d been lost; now I was found.

The sensation did not last long. The next day, Air Berlin was waiting to whisk me off to London via Berlin (31 euros, 65 euros with taxes and fees). The flight began on Air Berlin’s code-sharing partner, Fly DBA. The quarter-full 737-300 exuded shabbiness — tray tables opened crustily, and the color scheme was white and inconsistently green, with shades ranging from yellowish to kellyish to simply soupy, as in the shirts the flight attendants wore under black polyester jackets. The snacks, however, were great — breadsticks flavored with olive oil and rosemary — and as we approached Tegel Airport, we skimmed the clouds in a wide circle, the silhouette of our craft projected against the frothy white surface. Ah. ...

The next segment was on an actual Air Berlin plane, a spanking new Airbus A320 that was all computer-designed curves, with a gray color scheme that whispered sophistication. The air was so clean I could smell the high-tech filtering system, and for the first time I had a personal flat-screen, on which I watched “The King of Queens” and followed our westward progress across an ultra-detailed satellite map, all the way to Stansted, one of the London area’s four airports.

We landed around 8 p.m., and since my next flight was leaving out of Luton Airport at 6:30 a.m., a hotel room was pointless. Instead, I planned to prowl the streets all night with my friends Vincent and Weiting. Fortified with fish and chips, we set out across London from Vincent’s Bloomsbury town house, walking first to the Barbican Estate — a marvelous, messy, modernist apartment complex and arts center that is almost a town unto itself — then through the stately, lonely City and over the Thames to the Tate Modern. Maybe it was the threat of rain, but we saw no one else until we reached Waterloo Bridge, where a voluminously afro’d young woman was comforting a friend who’d had a lovers’ quarrel. They hugged and smiled for us, and at 3 a.m. we returned to Bloomsbury by cab.

Arriving at the airport tired and dirty is bad enough, but when you’re flying on RyanAir, it’s enough to make you suicidal. This was the airline friends had warned me about — not just the cheapest but the chintziest, not just no-frills but inhabiting a frill-free alternate universe. Still, when the London-Fez route is £1.39 (£38.32 with taxes and fees; $76.64 at $2 to the pound), who can complain?

I can. Boarding the 737-800, again at a distant gate, was absurd: seats on RyanAir are not assigned, and everyone made a mad dash for a good spot; all the while a flight attendant — in a blue uniform so crisp it seemed like she’d never worn it before — kept everyone out of the first six rows. They remained inexplicably empty the whole flight.

I settled in Row 7, then began to wish I’d never sat down. The cramped seats did not recline, and were made of molded blue plastic, as if they would be hosed down after the flight. Luckily, I’d been awake all night and fell instantly asleep.

RyanAir got me to Fez on time, however, and I even befriended my seatmate, a Canadian named Matt who said he was “studying terrorism” at a university in Wales. We shared a taxi to Fez’s medieval medina and spent much of the day exploring the labyrinthine marketplace together.

If I was going to get lost anywhere, I thought, it would be here, amid the high khaki walls and shadowy passageways to nowhere. Even before we entered, kids offered to guide us, warning, “La casbah est difficile!” I said I preferred difficulty — and plunged in. But though the market was enormous, with dead-end alleys and vegetable stands and near-identical knickknack vendors and swarms of schoolchildren who rioted with joy every time I pulled out my camera, I never quite lost my way. Even better, I felt comfortable — this was my kind of place, and I could have spent days or weeks drinking espresso with hash-smoking teens and stumbling upon the hidden ruins of pashas’ palaces. I left only out of exhaustion, but invited Matt to my hotel, a gracious courtyard house called the Riad Zamane, for a dinner of the best chicken tagine ever.

Next morning I was back in the air, this time on a 737-400 operated by Jet4you. My ride out of Fez, this tiny low-cost carrier — it flies between Morocco, France and Belgium with just two jets — had the highest fares (134 euros, or 144.09 euros with taxes and fees) and the oldest plane. The seats were threadbare, a chunk of my armrest was missing, and let’s not even talk about the stained fabric. The in-flight magazine was low-budget and unimaginative, and one of the French tourists on the nearly full flight was a middle-aged woman in a leopard-print top and tight black-leather Versace jeans. I closed my eyes and woke up at Paris Orly.

Ah, Paris! Now this was a place I knew well. Ever since I walked across the city one wintry night in 1994, my feet had developed an instinctual sense of the Haussmannian boulevards. I checked into my hotel, a cute, affordable Latin Quarter boutique called the Five, and headed straight for the Marais, where I found a pleasant surprise: winter sales! Virtually every store was offering deep discounts, and I took full advantage, picking up a Mandarina Duck suitcase to replace my venerable Briggs & Riley, which had lost a wheel under RyanAir’s care.

Getting to my flight the next day was a hassle. I was leaving not from Charles de Gaulle nor Orly, but from a little-known airport called Beauvais, about 50 miles north. (Colonizing third-tier airports is how many budget airlines offer such low fares.) To get to Beauvais, I took the Metro to Pont de Neuilly, wandered in a light drizzle until I found the bus depot, then rode an hour out to the airport, again befriending my seatmate, Gabriella, who like me was bound for Budapest on Wizz Air (6.99 euros, or 39.11 euros with taxes and fees).

“Oh, Wizz is the worst,” she said.

Not quite true, but Wizz, based in Poland and Hungary, was no Flybaboo. First, I had to pay an extra 35 euros for my overweight bag, now laden with 10 pounds of in-flight magazines, then the plane almost left without me. Inside, the air was overpressurized, and the flight attendants as confused as the color scheme, a mix of white and “magenta” that ranged from borscht to spilled zinfandel. At least Wizzit, the airline’s magazine, was entertaining: “The World’s Worst Food” was one cover line, and contributors included the travel editor of Wallpaper*.

Around 11 p.m. I checked into my hotel, but did not go to sleep. Instead, Bernadett, a friend of a friend, picked me up and we roamed the Hungarian capital in search of food — stacked crepes stuffed with mushrooms, tomatoes and cheese, and slathered in sour cream — and drink: Borsodi beers at Szimpla, a shabby but wonderful bar in what was once someone’s house.

The next afternoon, Bernadett and I drove up to Buda Castle, which looms gloriously over the city, and then to the airport. It was time for my final flight.

O easyJet, how I love thee! You may be a big shot, but in your Airbus A319, you treated me like a human being (for 5,950 forints, or 12,350 after taxes and fees, about $68 at 182 forints to $1). You looked the other way at my excess baggage, and though you don’t assign seats, you keep them spotless and roomy. Your flight attendants wore chic open-necked orange-and-gunmetal-gray shirts, and your in-flight magazine was professional and informative, with articles on percebes, the Spanish delicacy, and up-and-coming neighborhoods in Toulouse. “Come on,” winks your magazine, “let’s fly!” With you, baby? Anytime.

Alas, easyJet and I parted ways in Geneva. I grabbed a shuttle to NH, an airport hotel, and tried to sleep. I couldn’t. After a week of constant motion, I was buzzing with memories and inertia — I’d sampled so many places, so quickly, I wanted to revisit them all. Yet here I was at the end, in Switzerland on a desolate Sunday night. The adrenaline rush of disorientation was fading. Still, there was one ray of light: In the morning, I would be flying to Bulgaria. On Lufthansa. It was no low-cost carrier, but as I drifted off, I decided it would have to do.

WHERE TO GO ONLINE

Like all airlines, low-cost carriers often offer better prices to those who book early. Be sure to check all terms and conditions; these airlines often limit baggage and the changing of tickets after purchase.

FlyBaboo, www.flybaboo.com.

Sterling, www.sterling.dk.

Air Berlin, www.airberlin.com.

RyanAir, www.ryanair.com.

Jet4you, www.jet4you.com.

Wizz Air, www.wizzair.com.

EasyJet, www.easyjet.com.