Swift could hit Pokemon that used Fly or Dig, but only in Red, Blue and Yellow. Since the second generation games, it's lost that effect, and kind of lost its appeal with me.
Man... those attacks that lasted 2-5 turns really drove me insane in Red. I've been at the receiving end of many a Wrap attack. The good news is that these moves aren't 100% accurate, so there's a chance that you'll be able to actually fight back at some point during the onslaught.
For some reason, I was never really a fan of Hyper Beam. I don't know why. It does a lot of damage, but I'd prefer a more-accurate move that does half the damage and can be used over two turns to do the same amount of damage.
My favourite damaging attacks would be Flamethrower, Flame Wheel and Earthquake. Though I have to admit, Beat Up is extremely fun to use. My sister and I used to have battles in Pokemon Stadium 2 using this move, to see who could knock the other Pokemon out faster just by using this move.
My favourite non-damaging attacks are Double Team, Attract and Rest. Well, Rest has always been my favourite move. I like combining it with Sleep Talk in the second-generation games.