This is one of the best free games you will ever play. http://www.arma2.com/free
You need no personal info to register - a working gmail account, for example, is all the verification you need.
The shaky camera can be disabled for the motion sick amongst us :-)
The free version only differs from the full version as lacking a game editor (I think it also lacks full HD support) but if that bothers you the full version will set you back only $20.
It is slow-paced and very tactical. It is based on a simulator used by actual militaries, so bunny hopping Team Fortress/CoD/TF2 gameplay is definintely out. You can play as a squad leader (or squad member) or command platoons in strategic operations. You need to co ordinate your forces or death is very swift.
The orders you can give to your squadmates are quite fiddly (using F1-F9 menus and submenus). The full version is infinitely customisable. The publishers encourage modders and there are some excellent mods out there.
My only criticims is multiplayer is a little clunky - you can't leap into the action like a CoD style game. But those sort of players who demand instant pew-pew and scoreboard gratification (*cough* teens *cough*) are unlikely to be playing ARMA2.
This is close as a military simulator as you can come. It's basically a big box of military toys, and an enormous map to fight over (I'm talking 100s of km based on actual locations )
They're not perfect - they still use copy protection (who doesn't) but they even impress me with that - the copy protection stuffs up your aim in the game! Though they have removed part of their copy protection in a patch...
Give this a go - at 1 gig and a 250 meg patch download even its download is better than the 10 gig demanded by, say, Team Fortress 2....