Shin Megami Tensei series, almost all of them take place in either a modern day setting, post-apoc settings or in the case of the first one, both. The main series takes place mostly in post-apoc(though the first one has a big part in a modern setting), the persona series is all modern with a big focus on high school kids(except eternal punishment), the devil summoner games are action rpgs in an early 1900's settings i think and the Digital Devil Saga is a futuristic post-apoc game with cannibalism.
never played this but yeah
there's lots of random jap games about demons taking over tokyo or whatever that take place in modern times (well Shin Megami Tensei and like one other one but I think it's like kind of a cliched RPG plot over there for one reason or another)
I think there's actually a lot of rpgs over there that are modern settings just with supernatural forces creating the 'fantasy' part of the game, but the catch is you have to play as SAILOR MOON or some crap
somebody should make a redneck rpg like same idea as one of the above games aliens or hell demons are invading someplace in the US but instead of being some random teenager who gets magical powers you have to go to Wal-Mart and purchase beer and shotguns and there is a complex rib management system with over 1000 different kinds of ribs possible
you can also beat the game and start a New Game+ with Larry the Cable Guy in your party
Edit: Most of the games like Persona probably aren't modern so much as not-too-distant future and it's a rule that the closer in the future a game/movie takes place the more annoying the futuristic bits are. Like you picked up a book oh wait it's a CYBER-BOOK. Earthbound was probably like the only game that was supposed to be right now or at least only 2 or 3 years from now. It could even be slightly earlier time period because nobody seems to have computers in that game I don't think (or name better example of a recent invention that would've existed when the game was made)