For me Madoka Magica wins the "best ever" award, at least out of the limited selection of anime I have seen; as my only criticisms of it are minor nitpicks about the pacing of Kyoko's arc being a bit too fast; and the fact that the first episode is only really entertaining to rewatch, though it has the valid excuse of setting everything up so that the rest of the story actually makes sense.
Neon Genesis Evangelion wins the award for being my favourite anime, but certainly not the best, because it's a huge mess. But boy is it a glorious mess.
Serial Experiments Lain wins my award for best sound in an anime or... Well... Anything that isn't the Blues Brothers, to be honest, on the grounds of it having a great soundtrack and incredible sound design, both things which I greatly appreciate.
Azumanga Daioh easily takes my best characters award because, while it may not have any Homuras or Kaminas amongst its cast, it makes up for this by having a cast that pretty much entirely consists of great characters.
Although neither of them can compare to the voice acting masterpiece that is Angry Beavers, FLCL wins my award for best straight English dub of an anime, while Axis Powers Hetalia wins my award for best gag dub. Meanwhile, The Melancholy of Haruhi Suzumiya wins my award for best Japanese voice over track; and also wins an award for having a title character who is pretty much indistinguishable from me aged 15, bar her being rather more perverted than I was.
Death Note wins the award for most epic Potato Chip eating.