Syncing to another computer will make your iPhone sync to the computer's library. So you will lose your apps, but you always have access to your apps on iTunes after paying for them. You just need to log in under your account.
If you want to keep the settings of your apps (or high scores, etc) you should look into Chronus, a program available on cydia.
In the past when I formatted my PC I could copy over my library and stuff and retain all my on itunes when I synced. I can't remember if that included apps; all I know is that when I synced my iPhone with my new laptop, it removed all my apps. Maybe someone else can explain how to retain your apps (if possible), since I was in a rush for vacation and didn't have time to figure it out.

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