Every single game in Wadjet Eye's catalogue. Except Gemini Rue, which does contain three cover-based shooting segments. But three moments of violence in an 8-10 hour game is pretty reasonable.
There's also Broken Sword, Gabriel Knight, The Longest Journey... well, let's just say I really like adventure games and leave it at that.
I'm into visual novels, though some of them couldn't really be called 'games.' Then there's stuff like To The Moon or Actual Sunlight, but they're more like interactive stories. I suppose for the purpose of this discussion they're close enough to games. Hell, To The Moon has some rudimentary puzzles, at least!
There's also Uplink: Hacker Elite, which is a fantastic hacker sim. Very tense and incredibly fun.
Then there are all the Tycoon games; Rollercoaster Tycoon, Game Dev Tycoon (and Game Dev Story) and stuff like that. Theme Hospital and the like are great as well. Anyone know if Prison Architect is any good? There also appears to be a series of "Prison Tycoon" games.
I also like playing CRPGs none-violently when it's possible. Games like Planescape: Torment, Arcanum and the original Fallout are great for this.
Surgeon Simulator doesn't have combat =D Even if it is hilariously bloody.
NiGHTS is pretty incredible.
I really like racing games, and very few none-kart racers could be said to have "combat."
And there's puzzle games like Columns, Peggle, Bust-a-Move, Tetris... I don't mind rhythm games, either...
Come to think of it, a pretty substantial portion of my collection is none-violent. YAY FOR ME!