Portal 1 & 2 as a whole.
Amnesia: The Dark Descent (there’s violence but not on the part of the player).
Then again, these could almost count as modern takes on the adventure genre… Perhaps specify the point & click variety is excluded, while games like these which include potentially challenging real time gameplay count. Or something. I dunno.
Endless Ocean 1 & 2. Wonderful, beautiful, underwater exploration games.
Mirror’s Edge. Just running about and avoiding enemies is enough to finish most of the game. Though you often have the option of taking them on with or without weapons, that’s not the best part of the game. Bring on the sequel, EA.
PoP: The Sands of Time (2003), for similar reasons to your Tomb Raider example.
I suppose the 3D Legend of Zelda games count as similar to these too. Of course there’s a heavy emphasis on combat, but the designs of the world and puzzles are a joy too.
Well crafted 3D platform games like Super Mario Galaxy 1 & 2 also tend to be fun even when you’re not fighting enemies and bosses.
Side scrolling platform games, most of the good ones would be good even without killable enemies (some don’t even have any), just the actual levels and obstacles.
In stealth games like Thief II I like avoiding enemies, not taking them out silently, though, sadly, the more “modern” the games are the less of that you can usually do…
Retro RPGs, those with a story line, choices and consequences, the works, are fun to explore, though combat also plays a heavy role in them (though some allow you to avoid a lot of it via stealth or diplomatic options).
Strategy/sim games like Civilization II.
Well, I guess almost every game that is a little more involving than your average first person shooter has gameplay elements that are enjoyable without including any violence, which tend to be exploration, platforming, stealth, and combinations of those. Perhaps a tougher proposition would be to find great games that can exclude violence for the majority or all of the game, like the mentioned Portal and Sonic, without fitting under generally violence-less genres like point & click, sports & racing or puzzle.