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Aren't all of the clicker games like that? I haven't played any myself, but I think games like this match your criteria.

I haven't tried it out yet but I heard Mountain is pretty much like an interactive screensaver where you can also make music on your keyboard.
I think there is another one about Bonsai trees but I can't recall the name right now. Maybe it was simply Bonsai but I'm not completely sure that's the one I was thinking of.

Why you want to buy a game if you do not want to play it?

btt.: Maybe this http://store.steampowered.com/app/421040/ ?

I guess Plantera is a good example of that. Not the exact you want but similiar. İf you want to play there is plenty to do if you do not it runs at background.

Edit: Ninjad with 30 secs :o

Sakura Clicker kind of plays itself. :v

Clicker Heroes is a good clicker, if you don't know this one yet.
Viridi is a game where you plant flowers in real time.
Hero Zero is another free game where you have to wait 5, 10, 20, 30, 40 etc minutes to finish a "quest" to gain exp.

Adventure Capitalist: http://store.steampowered.com/app/346900/
Adventure Communist: http://store.steampowered.com/app/462930/
High Profits: http://store.steampowered.com/app/545650/

I used to play simple internet games and a game named coindozer on my phone. They all required not so much attention, because something was gained over-time (e.g. coins). As for Steam games I don't know, from the Steam Awards I do remember this free-to-play game Viridi, where you also get stuff over-time, like a seed once a week. How much attention your seed will need to grow into a plant and such I don't know, nor if it would be something your interested in. Given it was nominated, the game must have been doing something right :)

some tower defense games would be ok, you can build some towers and then wait for the next wave.
defense grid for example.

Progress Quest used to be fully automatic - you just start the game, and leave it running in your browser. No further action required. Your character will do this and that and level up while you either watch or don't.

this is a game made to idle if that's what you're looking for.
http://store.steampowered.com/app/452780/

Voodoo Garden
, or basically any level-based minimalist puzzle from Lyne through Zenge to Hexcells (though these rather wait for you while not doing anything, instead of doing stuff that would otherwise require you)

SimEarth.

Banished can be left alone once you've established a stable population and automated the trading docks.

Based on what you described I think that Tycoon-style games would be a great fit. Two of my favorites are also on Steam RollerCoaster Tycoon and Chris Sawyer's Locomotion, I would also recommend looking into Zoo Tycoon as it's another great one.

These are old games, but they have aged well, in my opinion, I played the hell out of them as a child and the cool thing is that once you built a few things, you can relax and let the game world evolve for a while before you tab back in and develop some more.

the sims :x
i mirco manage them sometimes , then i just let go alt tab and let them be/do what they want until i feel like controlling them again

Universe Sandbox ²