It was once impossible, but you can request new PokeStops, and to report PokeStops for various reasons, in Pokemon GO [Free]. The game's developer, Niantic, has created a support form where you can submit addresses to create new PokeStops or Gyms, either as a general request, or if there are none near you. As well, it's also possible to report a PokeStop if it's dangerous, if it's on your personal property, or if there's an issue with that location's PokeStop or gym.
Niantic shut down the Ingress [Free] request system back in September 2015, and as such, all PokeStops and gyms were based on that game's database, submitted by users. It has been difficult to submit issues with PokeStops so far. We've seen Pokestops at places where people probably shouldn't be playing Pokemon GO, like at Arlington National Cemetery, or Auschwitz. As well, people's homes have become Pokestops, which has been a problem for people seeing large amounts of unwanted traffic at their homes. As well, it's possible ? especially for suburban residents ? to not have anywhere near them to actually play the game! Niantic seems set to change that and improve the game and its Pokestop/Gym locations.