Watch it backwards!
Probably Digimon Tamers, since anything Lovecraft-related would be pretty bizarre backwards. I, obviously, wouldn't recommend one of those mainstream 100+ episode series.
Watch NGE backwards. You think that show's confusing enough watching it in the proper order? Let's take it Up To Eleven.
FLCL backwards. TOP THAT!
I think it would be prudent to ask this first: What anime have you already seen before?
Not too many, honestly. Though, I've seen the first episode of a lot of stuff, and never finished watching.
I guess Madoka?
Seconding Eva. That or Death Note.
Already seen Death Note, so that one's a no.
Hmm, level E's got some pretty good mind screws, and it's entertaining
I'm thirding Evangelion, but the question is whether you watch End of Evangelion first as opposed to 26, since End of Eva is meant to be the True Ending, regardless of how mindscrewy it is.
Ah. Personally, I think it would be interesting to begin with End if you end up watching Evangelion.
Since a lot of people are suggesting it, I'm probably going to go with Evangelion. Should I go with End of Evangelion or just episode 26?