You can read most of the forums without logging in. For instance, at the bottom of this forum it says:

Currently Active Users
3 (2 members & 1 guests)

The "2 members" are logged in (with cookies); the "1 guest" isn't.

If you want to post, to see members' profiles, or to do a number of other things, you will need to log in. As far as I know, logging in does set a cookie, at least temporarily. Without that, I don't think you'd make it past the first page without getting logged out again. If you check the "Remember me" box when you log in, your login cookie will persist even after you close your browser and will log you in automatically when you come back. If you don't check the "Remember me" box, I'm not sure exactly what will happen to your cookie nor exactly when it'll happen. There might still be a few crumbs left but there won't be enough cookie left to log you in automatically.

I log in from public computers only a few times a year. The one I use most often has a security feature that automatically wipes out my cache, history, cookies, bookmarks and settings at the end of the session. If it didn't, I'd clear the cache, cookies and history myself.