I second what everyone else said about Arcanum. However, I found replay value and side quest density to both be very low. Lower than Fallout 1 anyway. But they had plenty of great ideas and the setting was done very well.
Don't bother with realtime combat in Arcanum though. I found that I had to save between molotov throws because if I missed I had to reload the game and try again. Combat difficulty was THAT skewed. In realtime, you would die unless you completely overpowered the enemy - but even for weaklings I never really used it.
Planescape: Torment had hands-down the best written story ever. And if your character died, well, things happen. You're expected to die sometimes. You find out interesting things if you die
Like Planescape, Fallout 1 and 2 gave you the ability to make lots of different choices. But don't bother with other Fallout games, they're lame and not worth playing unless you're a rabid fanboy.
Until the end, I liked Secret of Mana. Unfortunately, a LOT of games tend to peter out around the midpoint. Secret of Evermore was, I think, slightly better even though it was enough like Mana to be a sister game. And it rocked throughout!
SNES Shadowrun was pretty awesome. The Genesis Shadowrun had better controls and was more true to the source material, but the SNES Shadowrun had better graphics and was a whole lot of fun.
Chrono Trigger holds a special place in my heart. The sequel Chrono Cross was not interesting enough to hold my attention past the first main story section. Chrono Cross had a ton of awesome ideas, but I guess it was just a tiny bit boring to me at some point. Your mileage will certainly vary.
Anyone remember the Genesis D&D game Warriors of the Eternal Sun? It was fun, though nothing mind blowing. Worth finding the rom (oops! I mean paying $120 for a soiled cart with a dead battery on ebay. Right).
I liked the old Gold Box D&D games. That and Dungeon of Doom were my first gaming experiences on a computer.
Wizardry 1 was pretty sweet. I remember reading about it in the computer game section of an old OLD Dragon magazine (like issue number 40 or something) and wanting to play it enough to search around for it for a while. Now you can find a SNES rom for Wizardry 1-3 ...
Morrowind rocked. But I feel like it had too little replay value. It's a game I would play through comepletely once with the best type of character, then maybe once again with a specific archetype and high difficulty, just rooting out all the fun hidden stuff (no, not HFS). But still once you talk with someone once you pretty much just skip their conversations. And you don't actually get to make interesting choices. Your choices tend to be "I will help you complete this quest!" or "I'll not complete your quest and you might try to kill me" or "I'll kill you or ignore you". For example, it was not possible to start your own merchant guild and take control of the silt striders and small boats and teleportation services.
More if I think of it I guess.