While not exactly LEGO, Nanoblocks (ナノブロック{nanoburokku}) are very popular in Japan, and they do have some of anime-related items. You could consider this answer a supplement to @bgrif's answer.
First, have a look at a comparison of LEGO (the big ones, of course) to Nanoblocks:
They're obviously a lot smaller, but the construction is still pretty solid, and given that they're more common than Mega Bloks ever were, I'd say there's some merit to their abilities.
Now, if you're still interested, there is a list of Nanoblocks available from Plamoya Japan, including a Pikachu (and the related Pokemon sets), though that's mostly it in terms of anime from them. However, there's lots of designer sets, such as those on this blog (Japanese), including Evangelion, Madoka Magicka, Doraemon, and others.
So, while you may not be able to find what you're looking for in LEGO, there's definitely other options out there.