It varies according to the 2nd link Kagehitokiri provided (and probably varies by state, but in Calif where the Uber lawsuit occurred. Excerpt:

[TAXICAB INDUSTRY
DE 231TC Rev. 3 (7-03) Page 1 of 3 CU
Taxicab drivers typically operate taxicabs under one of three business arrangements:
1. The taxicab company acknowledges the driver as an employee.
2. The driver owns and operates the taxicab, independently arranges fares, and personally pays for required licenses, permits, and insurance.
3. The driver performs services as a lease driver on either a fixed-fee or percentage-of-receipts basis.

Under the first arrangement, the taxicab driver is subject to the direction and control of the taxicab company and would be considered a common law employee (refer to Information Sheet: Employment, DE 231). Under the second arrangement, the taxicab driver independently makes business decisions related to the taxicab service. Since the driver is not subject to the direction and control of the taxicab company, the driver would be considered self-employed. Under the third arrangement, determining whether a driver is an employee or self-employed person requires a detailed analysis of the business arrangement. How the industry-specific details of the arrangement impact the employment status of drivers who lease a taxicab on a fixed-fee or percentage-of-receipts basis is discussed below."

From the HuffPo article:

"In the case, an Uber driver named Barbara Ann Berwick argued the company owed her money for costs she incurred while driving customers around in the car she owned.

In a normal employment relationship, those costs are borne by the boss, not the worker. But Uber considers Berwick an independent contractor, an increasingly common arrangement that shifts certain business expenses onto those doing the work. By using independent contractors, Uber not only doesn't have to buy SUVs and gasoline, it doesn't have to worry about payroll taxes or workers' compensation costs. That model hinges on the idea that people like Berwick are truly independent in their work -- a contention held by Uber and just about any company using the independent contractor model. Drivers are more akin to business partners than employees, the argument goes.

Barrett wasn't buying it. Uber, she said in her opinion, is the one holding the reins, "retain[ing] all necessary control over the operation as a whole." "Defendants hold themselves out as nothing more than a neutral technological platform, designed simply to enable drivers and passengers to transact the business of transportation," she said. "The reality, however, is that Defendants are involved in every aspect of the operation."

According to Barrett, Berwick was not owed any back wages, but as an employee she was due "reimbursable expenses" to the tune of $3,878.08, plus $274.12 in interest."

It's not going to topple the Uber model anytime soon, but is interesting.