That question has been debated since William Shatner still had hair.
I suppose people do it for the thrill of exploration. What about menial jobs though? Robots don't seem to be commonplace in the Trek universe. Voyager hints that holograms do some menial jobs but it's never shown or mentioned before that. Which means there's someone out there unclogging toilets, tending bar, or cleaning up puke on the holodeck. When they do have an episode set on Earth, regular humans are shown filling these roles.
You're not going to find very many people who would do these jobs voluntarily. Which means Earth's government probably has to assign jobs. Probably based on aptitude. The best and brightest are the ones who serve in Starfleet. The rest get lumped into roles that they're best suited at, or what ever is in demand at the time.
Now, under a communist system, you are still given a monetary reward for your work. The government pays you, and you spend your money at the government store to buy goods. In the Trek universe, money does not exist. All material needs and wants are provided for free via replicators. Health care seems to be free as well. Since there's no money, and no barter system shown, everything else must be free. So a person does not need to trade their labour for goods or services.
In that case, Earth's government would likely have to employ some sort of coercion to ensure menial jobs are done. Going back to Voyager, Tom Paris mentions there are penal colonies on Earth, and that he served time in one. Which means it's entirely possible that able bodies people who refuse to work are sent there as well.
United Earth maintains its utopia through fear and coercion. This would probably explain why there are no robots as well. Don't want too many idle citizens starting to wonder if there's another way of running things.