Insmonia, Immunity.
I simply chose what I think fit this Pokemon. I'd also like to reinforce that (imo) our goal should be not to make some broken ability, or choose the best ones, just choose the ones that look like they go with a mummy. :) I'm so very much against Sand Veil, we don't need another hax ability. T_T I don't understand at all how Air Lock fits this, and that's a Rayquaza exclusive (exclusives should remain so), so no. Dry skin might be nice... but I kinda like that as another semi-exclusive, and I don't know how a mummy in the rain makes sense, where an amphibian would. Immunity would be useful without being broken, too. Rough Skin is another cool ability that I'd be okay with, but... I don't know, there are more fitting choices. Shed Skin is a cool idea, but that would involve our undead friend taking off his bandages... eww. Synchronize just doesn't make a lot of sense, to me (but it doesn't on any Poke, really... but I guess it'd be more of a Psychic thing than a Ghost one). Snare Trap sounds cool, but what does he wrap with? His bandages? That doesn't make any sense, at all. If that were to be the ability, I think he'd need some extra loops of bandages hanging off from his wrists. But I don't think we need to make a "new ability" all the time. =\ If people feel the need to do that, I think something that makes a Ghost type Curse useful would be good, you know, since he's a mummy with a curse. Insomnia, to me, makes sense on a cursed Mummy, forever doomed to walk the earth (or something malicious... actually, it would be cool if the dex entry was the total opposite :P). I think that OU needs some more Insomniacs ('cause it will almost definitely be OU... let's make a niche UU, guys :( ), and he's still very prone to being WoW'd, taking prediction vs. potential double status sets up a notch. :)
Again, Insomnia and Immunity.