Most Bioware games do this:
Planescape: Torment is supposed to be incredible - most if not all fighting can be avoided. I haven't played it at all, though may need to in the future. Widescreen needs to be modded in.
If you don't mind the age, pick up the enhanced editions of the Baldurs Gate series. Yeah, they're worth it, especially if you want to try multiplayer with a friend.
Neverwinter Nights doesn't feature very many choices at all in the single player. If you're into roleplaying, there are still some great RP servers on Neverwinter Nights that are active. Combined with the DM client and toolset, some servers are almost like mini MMOs where your actions during DM-run events can change the world. Obsidian made a sequel which has some glaring camera and AI issues - I wouldn't really recommend it unless you have played all the other games I have mentioned.
Star Wars: KOTOR fits very well into the Bioware style of RPGs, and there is plenty of choices to be made as well. KOTOR 2 does as well, though it's not made by Bioware. Both games lack multiplayer support - you can mod it in, but it will displace some of the UI (the game's still playable). Also disable grass to avoid invisible character syndrome.
I've never played Jade Empire, but it's supposed to have Bioware choices too.
The Mass Effect series is, hands down, my favorite sci-fi RPG series. The first game is pretty rough gameplay-wise, but once you get through it both 2 and 3 offer great experiences. Yes, the ending to Mass Effect 3 isn't great. Yes, it's still worth it.
The Dragon Age series is great, every last one of them. Origins is a masterpiece, and Dragon Age 2 is definitely worth playing on a single playthrough (for best results, play sarcastic Hawke since they are very well written). Dragon Age: Inquisition has the best characters that modern Bioware has ever made (aside from Solas), and if you can get past some grinding that needs to be done, is a very fun game that is both different and familiar to Bioware fans.
END BIOWARE
Dishonored is a game all about choice. You decide the kind of person Corvo (the main character is) and your actions determine the fate of Dunwall as it struggles through a terrifying plague. Most of the choices in Dishonored revolve around your chosen playstyle rather than anything else. On one hand you could just slaughter everything in a revenge-driven quest, or you could maybe be a cold, calculating assassin. One valid criticism Dishonored has is that all-out combat is more enjoyable than stealth. For maximum enjoyment, I recommend two playthroughs, first stealthy and the other all-out combat.
Deus Ex: Human Revolution features some choices which do affect the story. Like Dishonored, Human Revolution is a mostly linear game but features some great level design as you make your way from point A to point B.
If you have any questions let me know, otherwise enjoy.