I've had my Droid2 for over a month now, and I've watched tons of youtube videos without a problem. I've watched 60 - 80 minute Flash videos with zero problem as well. Either you've got a lemon or you are in a slower 3G area. What are your SpeedTest results using the SpeedTest app in the Market? Depending on what part of the country I'm in, I've seen 3 bars of 3G get 2 MB down and 1.5 MB up, and I've also seen 4 bars 3G get 150K down and 50K up, lol, so not all 3G is created equal. If you are getting less than, oh, say, 700K to 800K download, youtube will buffer like a mother. Also, does it do it on WiFi too, or just 3G?
If you have a good fast connection, then that's not the problem. Try doing a factory reset, then before you load a single app or widget, try youtube. If your problem is solved, add one app at a time until the problem appears. If not...warranty? Although you'd probably have to "discover" a more serious problem to get a replacement.