In Red, I restarted my file several times (though I backed up most of those files), but since then, I've never restarted my "main" file. I grow too attached to my teams, and I haven't found a good way to back up the data for recent games, either (pretty much anything from gen III on, actually; if anyone has any reliable methods, let me know). I've started buying extra copies of the games so I can play them again, which is nice, though there are certain games I definitely play more than others.
It will be interesting to see how I feel when I get to the end of my current playthrough of VC Red. The idea is that I'll use it for challenges, and trade my Pokemon over to a storage cartridge when I finish the game, but we'll see how I feel when I get to the end of it, and how attached I've become.