Strategy as in RTS or strategy as in puzzle type games? I don't think that RTS games challenge the mind other than in those specific game conditions. Some puzzle games do on the other hand.
I used to play Stronghold Crusader, Rise of Nation, BattleField and Counter Strike...and now its time for Call of Duty....
I also like the game strategy. in addition to honing the brain this game also train our analysis capabilities and is very challenging