Second the recommendations for Ever 17 (even though I haven’t played it yet), and the Angel Smile titles (Heart de Roommate, Private Nurse, Figures of Happiness).
If you like strong story in your game, play Nocturnal Illusion. It’s dirt cheap, and (assuming you make the obvious choice) you can get all the endings on one play through. (Once or twice, you’ll get asked a question like “which one of us do you like better, A or B?” while they’re both present – gee, that’s a hard one Be warned NI is very old school, because it is a very old game; as I understand it, it was one of the first b-games to be more than a sexfest (yes, THAT old).
I would also add that Hitomi is a dark game, so I haven’t played it.
You might also like Brave Soul, it’s different. An RPG. There’s also Pretty Soldier Wars (the other RPG that just came out).
Critical Point actually has totally different explanations for what happens, depending which path you end up on. (That is, the overall story is different! There’s still a ‘main path’ though, and it’s pretty obvious why when you play.)
Doushin I have yet to play, but it has an interesting branching plot structure.
Games that are NOT recommended, given your description: Snow Drop, Little My Maid, all 3 of the GC series (Kango, Horny Bunny, and Come See Me Tonight), and Tokimeki Checkin!. While many of these games I like, they suffer from a repetitive structure.