I play them often. I like Tsukihime, True Love (Although that's more like a dating sim...), Fate/Stay Night (Although MM's silliness is preventing me from playing my fucking Heaven's Feel route! Dammit, Message...), Narcissu, and Anon's Nice Day. I'll start on Clannad, OMGWTFOTL, Ever 17, Yume Miru Kusuri, and Kagetsu Tohya soon.
For those that are not in the know, here's a comprehensive list of translated visual novels. Also, the actual game usually isn't packaged with the translation patch. For that and the musical scores/voice work, look it up on /rs/.
As for Phoenix Wright, I used to like playing them a lot. However, now that I've played a few different VNs, the AA series feels like Baby's First Visual Novel. It's very linear, and it's also impossible to get a bad end. I also find the character progression to be lacking, since there are always characters coming in and going out. Most of you guys have flash cards such as the R4, so consider playing some of the VNs that have been ported to the DS instead. You can find the .nds file needed to play VNs, and the VNs here.
I'm glad I stumbled upon this thread. It's refreshing to see a visual novel thread amidst all of the FFVII and Halo shit clogging up the Video Games board. I suppose I'll start coming here more, so that I don't miss these rare threads.