AHHHH! I forgot about Warning Forever. Never really got any good at it but the graphics sort of force you to unfocus to succeed.
My go-to zen games are Hotline Miami and Super Hexagon. Both are games that punish you if you hesitate for even a second. My best runs have been times when I've reached a mental state where I don't even consciously register what's onscreen, I just react.
Dark Souls is a weird game for me, especially the boss fights. Sometimes I'll just rely on dumb luck and win by the skin of my teeth. Other times, my brain will completely synch up with the game and I'll time every block, dodge, and attack perfectly.
Playing Just Cause 2 is a great way to sit back and let time wash over you.
Whenever the beta servers for the multiplayer mod are online, I zone out in JC2 for hours just driving around and messing with the physics. The best experience I had was an hour long drive through the mountains with some random other player. We never communicated or attacked each other, just enjoyed the scenery.
Minecraft, Forza Motorsport, Team Fortress 2.
I also find collecting things in open-world games to be very relaxing, so any sandbox game with collectables would also count.
And, fittingly, I loved the Zen Garden in Plants vs. Zombies, but unfortunately when I got a new computer my Steam save was lost and with it, all drive to play that game again, lost a 40-hour save file. Can't fucking wait for the sequel though.
That would be The Dishwasher: Vampire Smile for me. The story is awesome, but is nothing you need to pay attention to to enjoy the gameplay. The gameplay, I might add, is perhaps the most fun I've had in a video game in a long time. It's one of the only games I continued to play after I got all of the achievements, which should be a testament to how fun it is. I even went so far as to write a blog post about it. It destresses me that much.
Vagrant Story, more recently Dark Souls, Starcraft: Brood War. And of course Freecell. I don't really get stressed out but I certainly relax while playing the above games.
Being a chronic insomniac, I have a couple games that require little to no skill that I play when trying to relax and sleep. One is 'Solar 2,' and honestly it's the only game I have that I can play whilst lying down on my couch. Hell, I've actually fallen asleep playing it. On the other hand, if I've just woken up and have nothing to do for half an hour or so, I'll toss on Super House of Dead Ninjas. It takes considerably more concentration but little thought (as my brain has about a 45 min boot up cycle...), and it kills time with no questions asked.
I tend to tire of games after a while, but i'll usually have at least one "zen" game at a time. It was Minecraft for a while, then probably Fallout: New Vegas. It was FTL for the last few months and weirdly enough i've now landed at XCOM: EU. Just the whole nature of "Alright, you're going to pop in here for a mission, move forward a little, and all actions are permanent so if you fuck up, don't sweat it, just go with it" is appealing to me.
I'll tell you what game isn't going to join my zen pile, Valkyria Chronicles. Cheating piece of shit AI.