VERY IMPORTANT: When Purchased a game from Steam, Steam save my game? READ DERSCRIPTION!!?

0kay,I want to purchase a game on Steam. Like CSS or TF2. (I love Steam games). So if I purchased any games on steam,will it save? I mean if I get a new computer,and my steam has gone,will my game gone forever or it will be installed when I install steam???
Update: EDIT: Dr. Ibis winner.
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