Keep in mind some of these may not be the most wholesome, but they are good and mostly non-violent. I'll read the ones off of my Steam library and give a small description:
Battleblock Theater - A fun little platformer with co-op. Rare potty humor but otherwise fun to play.
Hollow Knight - A bit of fantasy violence and a dark setting, but as you play you help out cute little bugs and stuff. I hate comparing games to Dark Souls, but it's like the Dark Souls of platformers mechanics-wise.
Ori and the Blind Forest - Another platformer, this one is really fun and lighthearted. Excellent visuals and sounds give a beautiful story with few words. I'll admit that I cried in the first 10 minutes of it.
Portal 2 - A classic Valve game, very light swearing and violence but some are still there. It's more of a puzzle game with some humor (sometimes dark). This is a must-have for a lot of gamers, but most of the game isn't necessarily wholesome.
Project Cars 2 - A racing simulator with a lot of variety. Requires a decent rig to run. Huge variety in races, from F1 to Rallycross. It also has a ton of available cars to race in and multiplayer.
Rocket League - A popular game for a good reason, Rocket League is soccer with cars. You can play against bots but the real game is in the multiplayer, this means you might meet some bad apples.
Civilization V - Not violent on a personal scale, but you are capable of going to war and even nuking other players. You can also play diplomatically, and try to win through methods like a cultural or diplomatic victory. Not necessarily wholesome, but mostly non-violent and a very popular strategy game.
Space Engineers - Like Minecraft but in S P A C E. Build tons of spaceships and stuff. I'm not good at any of that though, so I get my cool ships from other players on the Steam Workshop. It has multiplayer too. Not at all as in-depth as Kerbal Space Program, though.
SpeedRunners - A fun party game where you and up to 4 other players race around a map collecting power-ups and swinging over gaps. Eliminate players by forcing them outside of the screen. Last player left wins, and it's best of 3. Not that fun unless you have other people to play with, though.
Subnautica - Don't play if you're scared of the ocean. This is a survival game set on a vibrant water world. You can build underwater bases, scavenge supplies from your crashed ship, explore a somewhat dark story (I haven't gotten that far through the game yet), etc. Most violence would be killing fish with a knife (no blood) or hitting them with a submarine (also no blood).
Tabletop Simulator - A multiplayer board game simulator. Play any game you want, you can find almost every game imaginable on the Steam Workshop. If it's not there, you can make the game yourself pretty easily given available tools. I've played bootleg D&D with a random group of people off the Internet, played Guess Who? with a guy from Kazakhstan, and organized a few games between me and my friends.
I'll list a few games I don't own that might work too, you may or may not be able to find these on Steam:
FTL: Faster Than Light
... (This is what I could think of off the top of my head, sorry it's not much)
Steam games with the tag "Family Friendly" --> http://store.steampowered.com/search/?tags=5350