While not all the stories are brilliant, Rin & Emi's stories both do things I've never seen done in the genre, going places I would expect to see only in a quite good movie or book.Rin's in particular has some simply amazingly powerful scenes.For instance if you go to little busters you will see Fluffy listed.Fluffy is a translator, so it lists licensed and fan translated. Which will show you how popular Clannad and Fate stay/night are two of the top games out there.Edit: if you aren't interested yet, at least read the write-up: goal of /r/Games is to provide a place for informative and interesting gaming content and discussions.Submissions should be for the purpose of informing or initiating a discussion, not just with the goal of entertaining viewers.
The latter two have an anime out already and little busters is getting one this fall. An english patch to the PC version was relatively recently released.
Make sure to leave the adult scenes on, at worst they're funny filler, at their best I can't imagine the story without them. Persona 4 is basically two games, a dating sim in the real world, and a fantastic jrpg in the tv world.
The way the mesh the genres just enough while still retaining their separate flavor is impressive. You can also look around in the OELVN community, on the Ren'py site I think, for some free dating sims.
If you play YMK, don't start with Aeka's route.edit: Added a link to the RE: Alistair site. Princess Waltz is pretty awesome in terms of story and characters, but it doesn't have much in the way of player input (outside of its surprisingly fun card-based battle system).
Not for the homophobic, though, as the main relationship is not the straightest thing you'll ever see.