Of course, as usual, I'm not going to pick just one. But I will limit myself to 5 and will only pick opening of series I have actually seen.
Let's get the most obvious choice out of the way right now.
Yes, I know, very predictable and something that pretty much everyone picks, but hey, it's just that good.
But now some lesser know openings (at least somewhat).
Death Note 2nd opening
Ghost in the Shell: Stand Alone Complex 2nd GIG opening
xxxholic 1st opening