Browser Based Games

RuneScape

Armor Games there are bunch of great games :) i recommend Kingdom rush and operation stranglehold

I think there is 100s of strategy browser games that looks exactly the same, like Tribal Wars and Desert Operations.

atWar is like Risk but online and non-linear moves.
Dead Frontier is fun but after a while it gets boring scavenge every buildings.
Runescape is not as good as used to be.
BF Heroes is kinda balanced between F2P players and Premium players. BF P4F is not.
Quake live. Is Quake, no need to description.

well, I can't think in more browser games :P

I have been playing Card Hunter recently, it is a good mix or turn based RPG and card based combat (Magic style). It is completely F2P besides

Card Hunter

You could always try the demo for Creeper World 2 (it's somewhat different from the first one). :D
There are also the Crush the Castle games (although those aren't exactly strategy).

FunOrb used to be great (and still is I guess) but then its devs ditched it. Just don't get too attached to any games there, they aren't seeing updates any times soon. Shattered Plans, TerraPhoenix and Zombie Dawn are really good strategy games there while Orb Defence is a nice tower defense (I usually put those in a genre of their own).

strategy in it's purest sense.

Hail Caesar

Transformice
It's not strategy, but still very fun.

erepublik?