Most of the online games require a monthly fee to be played because the costs of the maintenace of the servers and the cost of new servers is quite high...I must have in mind that FFXI and WoW for example are MMORPG that need a very good internet connection and a very good server to be played...But there are games that do not need a monthly fee like NWN (NeverWinter Nights), Guild Wars, etc...For more info on MMORPG go to this site:
MMORPG