Absolutely! Many characters are written as living on planets, or on stations. (Many were also born on stations.) Most capsuleers don’t live in their ships/pods.
It’s also possible to visit planets; for example, many players RPed their characters as being on Thebeka III when the trouble unfolded a few months ago. And Thebeka III is at least one character’s home planet. Similar happened with Anath, and plenty of other CCP-created events.
Several of us (well, our characters) wrote stories set on planets or stations for the New Eden Capsuleer’s Writing Contest; feel free to check them out if you want some examples! There’s also lots of other writings on the Player Fiction board.