The more recent Anno games (or Dawn of Discovery) are very laid back and relaxing without beeing boring. It has a very slow learing curve and at least the campaign will never frustrate you. With DoD Gold Edition you will get -hundreds of hours- of gameplay (I kid you not) if you like those kind of games.

Haven't played Anno 2070 yet, but it looks even better.

There's a previously commercial (now freeware) game called [url=http://www.matrixgames.com/products/237/details/Titans.of.Steel:.Warring.Suns]Titans of Steel: Warring Suns[/url]. It's played like the traditional tabletop version of Battletech, on a hexcell map, and the action is switchable between realtime and turnbased. There's an easy to use mission editor in there somewhere as well.

http://www.gamersgate.com/DD-MONTJOIE/montjoie

http://beta.indievania.com/games/didgery

http://store.steampowered.com/app/34500/?snr=1_7_7_151_150_1

http://www.gamersgate.com/DD-BELDEL/bellatorus-deluxe

Romance of the Three Kingdoms series (before XI). RotK online is the best one but requires using credit card to purchase in-game currency to actually get anywhere.

Trying to think of games that are not real time and not commonly known.
There are a few interesting ones for PSX Emulation if you are so inclined:

Chocobo's Dungeon 2
Saiyuki Journey West
Azure Dreams
Hoshigami - Ruining Blue Earth
Torneko - The Last Hope

and my personal favorite PS2:

The Tower of Drauga






Thanks for that and also check Cryptic Comet:

http://www.crypticcomet.com/

Yes, this, just do not download it right now as it's going to be patched again during next week.

How about:

Disciples: Sacred Lands

Disciples 2

Somewhat simple but fun fantasy turn-based strategy games with a fantastic art style.

The most chill managerial sim I ever played is Pizza Tycoon, followed up by Sim Theme Park. See if you can get your hands on either of those.

Another one is Space Rangers 2. Avoid the RTS part (which, love or hate, is most definitely not chill. Other than that, just flying around, scooping up minerals and leeching off dead Dominators away from other Rangers while enjoying the calm music and typical everyday happenings of space travel, is really relaxing.

I also second MOO2. The music is really chill. One up for Plants vs Zombies too, now that's a game you can play if you're stressed out.