Attract+Nasty Plot.
I don't know why, it's just funny. My Houndoom pulls it off so nicely.
Of course, what would be even funnier is Attract/Charm/Captivate + Scary Face/Mean Look. Seems like the latter should cancel out the former, doesn't it?
One of my favourite combos to use is a status-problem move + Hex. I just feel so evil when my Pokemon does lots of damage with Hex thanks to the target having a status problem. It looks especially cool if the status-inducing move is Will-O-Wisp. My Chandelure knows this combo, and I don't want to teach it Shadow Ball to replace Hex.
Another combo I like is Cosmic Power/Defend Order + any HP-restoring move. Usually I alternate the two, and then my Pokemon becomes a super-wall! I had two Pokemon that used this: a Clefable with Cosmic Power and Moonlight, and a Vespiquen with Defend Order and Heal Order.
And here's another one my Excadrill likes to try out: Hone Claws + Horn Drill. Not as uber as Articuno's Mind Reader + Sheer Cold (or my old Poliwrath's Mind Reader + Fissure), and it doesn't always work, but I like to try it out on wild Pokemon, and the OHKO moves are fun to watch.
In a double battle: One Pokemon uses Fake Tears on an enemy, and the other uses a Special attack on the same enemy. Also works with Screech + Physical attack. Only works if the debuffing Pokemon is faster of course. In Colosseum I used to have my Plusle do the Fake Tearing a lot.
And here's one I haven't tried yet: Soak + any Grass or Electric attack. Or Soak on a Flying-type + Earthquake. Either of those will be fun...
Another one I like is Future Sight + Recover, which I have on my Reuniclus. Use Future Sight, and while the foe is attacking, spam Recover until the attack hits.
Also, I miss the move combos you can do in contests of R/S/E... Those games had the best contest system IMO.