In eight major cities, including New York, Paris, and Washington D.C., three-year-old startup Uber is trying to remake the cab experience. Drivers aren’t employed by Uber, but get a cut of each fare instead. The arrangement can be lucrative, bringing in upwards of $500 a day, a sum some cab drivers only make after a week’s work. Rates take into account the typical factors of time and distance but — through an Uber-developed algorithm — also demand. Uber’s servers crunch information about where riders are requesting cars, where they’re likely to want to go, even traffic-distorting big events nearby. When a Giants in San Francisco game lets out, several Uber cars are likely close-by.

The man behind Uber is Travis Kalanick. The company’s co-founder and CEO doesn’t look 35 save for some salt and pepper, a souvenir from a previous venture. “What we like to say is FedEx delivers packages tomorrow, but Uber delivers packages in five minutes. It just so happens that that ‘package’ is a towncar that takes you wherever you want to go,” he says. Kalanick has a tendency to punctuate his sentences with a big grin and, when he is talking about work, his speech is electrified by cocky self-confidence. “In the beginning, it was a lifestyle company. You push a button and a black car comes up. Who’s the baller? It was a baller move to get a black car to arrive in 8 minutes.”

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Kalanick’s office is anything but plush, however. Uber’s San Francisco headquarters is spartan to the point of being nondescript. Kalanick holds court in a small corner conference room with a transparent wall. Complex-looking equations are scrawled across the glass. Those who know Kalanick describe him as hard-charging, sometimes awkward, but not prone to the meanness of some successful entrepreneurs. It’s hard to quantify how much the market Kalanick is going after is really worth, though the company estimates it is a multi-billion dollar opportunity in the United States. Uber has provided hundreds of thousands of rides so far. More significantly, Uber users are spending over $100 a month on average on the service — an astonishing figure compared to the minuscule purchases most apps encourage. The company has raised more than $50 million in funding so far from backers that include Bezos Expeditions and Goldman Sachs (GS).

A month after I visited Kalanick’s offices, Ron Linton, D.C.’s Taxi Commission chairman, accused the startup of operating illegally and made news when he helped orchestrate a sting, hailing a car via Uber and sending it to the Mayflower Hotel. There, city inspectors ticketed the driver for four violations, including driving an unlicensed vehicle, not holding a chauffeur license, and charging an improper fare. The driver was fined $1,650 on the spot, but the incident sent shockwaves all the way to Uber’s headquarters in California. Taxi interests around the country, it seemed, weren’t so happy with Kalanick’s model. It was a potentially disastrous turn for the fledgling company. In today’s skittish climate, anything that knocks a startup off message or gestures at a fundamental flaw in its business model can have serious repercussions. To wit, Groupon (GRPN), Airbnb, and Zynga (ZNGA) all had to trim their sails due to early snafus.

D.C. may have picked a fight with the wrong entrepreneur, though. In one sense, Uber is the result of 14 years worth of entrepreneurial misadventures on Kalanick’s part. In 1998, he dropped out of UCLA to work on a peer-to-peer file-sharing program similar to Napster dubbed Scour. With funding from Ron Burkle and Michael Ovitz’s CKE Associates, Scour seemed headed for prime time. It wouldn’t end well. Scour got into a scrape with Ovitz over their term sheet, which eventually lead to a settlement Kalanick still bristles over. (“That matter was amicably resolved years ago,” says James Ellis, Ovitz’s attorney and former Scour board member.) Then, in the summer of 2000, Hollywood served Scour with a lawsuit claiming a whopping $250 billion in copyright damages. Though the suit would be settled for $1 million out of court, the company went bankrupt. Kalanick was scarred. He couldn’t watch a movie in the theater for months; the sight of a studio logo set his blood boiling.

Still smarting, Kalanick tried again. In 2001, he co-founded Red Swoosh with partner Michael Todd. Officially billed as a file-sharing system for corporate clients, Kalanick says he intended Red Swoosh as a “revenge business.” He wanted the Hollywood litigants who sued Scour into nonexistence to pay for a similar technology. But like Scour, Red Swoosh ran into problems. Without his knowledge, Kalanick says his co-founder sought to abandon Red Swoosh and take the engineering team to Sony (SNE). (Todd disputes this claim.) Worse, the company ran out of money in the fall of 2001. Kalanick spent those years not paying himself, desperate to keep the business afloat. That meant living with his mother again in Northridge, a suburb outside Los Angeles. At one Consumer Electronics Show, he slept in a rented Toyota (TM) Sienna, giving himself hobo baths in the restrooms of nearby casinos. “There weren’t a lot of ladies during that time period,” he jokes.

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By 2007, things had turned around. When Akamai Technologies (AKAM) acquired the company for $15 million, 23 of the 29 Hollywood litigants who had sued Scour either had content flowing through Red Swoosh or had become clients. And that may be the key to understanding Uber’s current predicament. Kalanick, as well as brilliant, is brash and headstrong, even happy to charge off a cliff with an innovative idea. With Red Swoosh it paid off with a multimillion dollar acquisition, but only after years of struggle. (An ex-girlfriend calls him “the unluckiest successful entrepreneur ever.”)

Uber, meanwhile, is more than a fast-growing business or the flavor of the moment with the San Francisco technorati. Many companies still use the now ubiquitous geolocation feature in mobile devices for relatively rudimentary aims — checking in, virtual badges, coupons. Uber’s ambition is not just commercial. It wants to revolutionize the country’s seventh largest transportation system. And that has earned it plenty of evangelists. Comedian Dave Chappelle and actor Edward Norton are fans. Venture capitalist Marc Andreessen, who is not an investor, calls it a “killer experience.” Airbnb CEO Brian Chesky adds, “Uber makes it very easy to not own a car.”

Still, Uber faces plenty of challenges. For one, the price of an Uber ride can be steep. Average fares cost up to two times as much as regular cab fares. A ride that may tally $13 in a typical yellow cab could clock in around $26 via Uber depending on conditions. On holidays, when demand for cabs far outstrips demand, fares may climb even higher. In fact, its pricing model proved controversial on New Year’s Eve when one user was charged $75 for a two-minute, half-mile drive. In all, more than 95 users complained. The company was forced to refund fares on a case-by-case basis. “We took our lumps, and we learned a lot from them,” says Ryan Graves, Uber’s general manager and vice president of business operations. In the future, the company says price notifications to be clearer.

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Ultimately, Uber’s biggest challenge may be with municipalities. In late 2010, the same day Uber’s board made Kalanick CEO, the San Francisco Municipal Transportation Agency demanded the company cease and desist operations. Because Uber was allegedly running and marketing itself as a cab service but without a permit, the company was threatened with fines, including $5,000 for every transaction it made. The next day, the startup dropped the word “cab” from its name. So far, that has appeased local regulators.

D.C.’s beef with Uber may be harder to resolve. “Uber was so disrespectful to the District of Columbia, that they didn’t even bother to check and vet their drivers to make sure they were all legal,” Linton says. He also cites a city law that requires cars that charge by time and distance be licensed as taxis. This supposedly conflicts with Uber’s pricing model. Kalanick claims Uber checked with the commission before deploying in D.C. and got a green light. “When we enter into a city, we don’t take that responsibility lightly,” he says. Democratic Councilmember Mary Cheh, who chairs the D.C. Council’s Environment, Public Works, and Transportation Committee, was surprised by Linton’s actions. “It was too quick, too precipitous, and not the way I like to do business,” she admits. Uber is consulting with local attorney A. Scott Bolden, who says they’ve done nothing illegal. Now, Kalanick and Linton have a meeting scheduled to air their grievances face-to-face in mid-February.

To grow, Uber must find ways to make its service jibe with the gnarl of authority in different cities. Taxi systems almost always feature a large group of players motivated by varying interests, not limited to cabdrivers, medallion-leasing agents in some cities, and regulators. It isn’t lost on the company that some taxi systems have resisted adopting relatively simple technologies such as credit card readers, let alone what Uber proposes.

For the time being, the company is continuing to plot its expansion, rolling into at least 18 new cities by the end of 2012. It also plans to offer car types at different prices, a more expensive SUV for large groups or a cheaper hybrid option for the price-conscious for example. If in the process, Uber ends up ruffling more feathers, that’s all right by Kalanick. “I like shaking things up in an old industry and making something new and different,” he says. “I like pissing people off.”