I'll just add my two cents here.
My favorite visual novels include:
Tsukihime
Fate Stay/Night
999: Nine Hours, Nine Persons, Nine Doors
Kira Kira
Clannad
and I liked Hotel Dusk: Room 215 pretty well
Time Hollow is okay, and I'm not sure if the Phoenix Wright games count, but I love those. If you're a fan of visual novels, I'd suggest checking into the lovely little genre of "adventure games," which is my absolute personal favorite out of anything I could play (too much incredible survival horror not to be). They also tend to bleed over into the "puzzle game" zone, though, so I suppose it depends on your style.
Another thing, if you would be open to it, is to check out the old text-based novel/adventure games. Most of them run on DOSBox, but if you can get past that, there is some absolutely mind-blowing content available there. (If you decide to look up any text-based games, do go find one called "Anchorhead." I'd just like to say that that particular game is one of my absolute most favorite games of all time. It is just a totally fantastic, engrossing story, and there are a lot of paths to go by, though not as many endings. It is well, well worth your time, though.)
Other than that, I'd say if you'd like to go hunting or want to really get into these kinds of games, you should start by checking here:
http://vndb.org/
and here:
http://www.adventuregamers.com/