I've played quite a few non-combat games:
The Neverhood Chronicles is (mostly) devoid of combat. Gameplay consists of just exploring the world and solving puzzles. The only times someone or something dies is during a cutscene, which is a rare occurance.
Most puzzle and adventure games fall under this category, such as Tetris, Yoshi's Cookie, Bejeweled, Tetris Attack, Myst, anything made by Telltale Games, etc. Most music and rhythm games are non-violent as well.
When I play Minecraft, I tend to shy away from fighting the monsters that come out at night. I just enter the safe house I carved into the side of the mountain and wait for daylight to return, often taking the time to craft the various ingredients I've collected. I will defend myself against any spiders or creepers that stick around, however.
Even games that have sizable combat aspects can have engrossing non-violent segments. For example, when I play Bioware games I often find myself enjoying the NPC conversations more than the actual combat. I once spent over an hour on KOTOR just wandering through the Ebon Hawk, talking to every party member and listening to their stories and bits of advice. Mass Effect took it one step further with its exhaustive encyclopedia on just about everything. It has enough lore in the first game alone to rival well-established sci-fi settings that have been around for decades.
Dont expect others will adhere to this though so you may want to take cover from time to time.
