It's not clear whether the OP is looking for soft wrapping or hard wrapping. If it's just soft wrapping you're after, that's easy: turn on View->Soft Wrap (as Steve said) and set the View->Wrap Column to 80. This will wrap the lines at 80 columns no matter how wide your window is.
Be aware, though, that this will *not* put a line feed at the end of each line. Such "hard wrapping" is traditional in Unix text editors, but not in Mac editors. TextMate follows the Mac tradition and doesn't have an automatic hard wrapping setting built in. In addition to the previous suggestions, you could also create a command with
1. Save: Current File 2. Command(s): fmt -w 80 3. Input: Entire Document 4. Output: Replace Selected Text
Binding this to ⌘S will hard wrap the document to 80 columns every time you save (assuming you use ⌘S to save rather than the menu).
For what it's worth, I used hard wrapping in my Linux days, and it always screwed up the non-Linux users I shared text files with. Since moving to the Mac, I've gone with soft wrapping and never looked back.