if your talking about an RTS then age of empires or company of heroes. if its an FPS then Call of Duty or borderlands or even oblivion for the LULZ. if its none of these or you don't know then you shouldn't even play online games.
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Amazing game :)
It's called Grepolis, you build a city and conquer the lands around you with the help of you alliance.
Paste this into your search bar:
http://en.grepolis.com/invite-4024929-en58?invitation_id=410883&invitation_mac=d7b41164&ref=player_invite_linkrl
There are various online strategy games that range from being more socially geared, like the casual ones found in appstores, to more intensive ones that can be played in both single and multiplayer mode like Starcraft II (critically acclaimed). For browser based ones, some of the most played and reviewed include Battledawn, Supremacy 1914 and League of Legends.
By war game do you mean a real-time strategy? If so I would reccommend StarCraft for the PC.
Call of Duty or Battlefield in my opinion are the best... battlefield will be more realistic though