What are the rights that a felon looses?

In the United States:
Rights are things protected in the Constitution (the founding fathers believed that the rights themselves were granted by god, and as such the government is not able to restrict them). This list includes rights as well as privileges. In addition, while not asked, most states have a process to restore those rights (when the conviction was in that state), each state has its own rules. The federal system has no formal process for expungement except for very specific minor drug offenses.

Some states (based on where you are registered) restrict the right to vote, other states allow you to vote as soon as you are off probation, supervised release, or any other monitoring service.
Certain crimes make it difficult if not impossible to get a passport, however most felons are eligible to receive a passport.
Some crimes make you ineligible for certain positions of trust (usually government jobs), they can make getting a security clearance difficult (its based on points, the conviction alone does not bar you, but its enough points that its likely you will be barred for some time after the conviction)

18 USC 922(g) prohibits owning firearms, ammunition, and ammunition components.

California restricts getting a commercial drivers license (the patriot act requires a background check I do not know what all that restricts), commercial drivers licenses are required for privately owned motorhomes larger than a certain length.

California restricts being a nurse, paramedic, and a few other jobs.

Bar associations also generally restrict anyone convicted of a crime of "moral turptitude"

License to practice medicine may be restricted to those convicted of certain types of crimes.