I'm going to the assume the topic in question means "killing in general" not specifically humans.
In which case... that's very difficult to think of games I own which don't involve killing.
Only games I own which don't involve killing are:
The Sims 3 (Technically you can murder people if you want.)
Maniac Mansion II: Day of the Tentacle (Oddly enough, no death is involved despite Purple Tentacle wanting world domination. The original Maniac Mansion however had plenty of death.)
Myst series (Technically has themes of death in a couple spots, but c'mon I don't have much to work with here!)
Theme Park World
Other ones I've seen mentioned:
LittleBigPlanet
Katamari Damashii
Portal
I own both of these, however, LittleBigPlanet certainly has killing of enemies and bosses (similar to other platformers like Mario etc.) And Katamari Damashii may as well have killing in it because you're rolling living creatures and objects into giant balls and throwing them into the space to become stars. I can't imagine any of them would be alive after that. Portal I also own, and while it's generally not the point, there's tons of themes of death and you do kill Glados and your best friend the Companion Cube.
Otherwise, the entire rest of my collection is hundreds of various murder simulators (as Jack Thompson would put it.)
As for which one I played the most recently.... Um... The Sims 3. I haven't played the rest of these in a long while.