I wasn't aware that there was an anime review section to the Escapist, despite being a member for almost 2 years... I feel kind of bad for not checking out these reviews when they were new, but having read a few, I believe most of them still apply (if you can ignore the "the second bit comes out soon!" bits).
Birdy: The Mighty was my 2nd favorite anime (1st being Ghost in the Shell) until I watched Zero no Tsukaima, but that doesn't mean it is bad in any way. Birdy is still an amazing anime that I recommend to everyone I know who likes anime. It can be silly, serious, light hearted and grave all in the same episode, and as JoshV says in his review, each episode foreshadows to the next and almost forces you to keep on watching. Reading this review almost makes me want to watch both seasons right now, lol.
The only problem I have with Birdy: The Mighty, is that it is too short. The plot that is developed in the first season comes to a satisfying conclusion in the second season, but there are still some sub plots and factors that are unresolved. Yes, these factors may be small and insignificant compared to what happens in the first and second seasons, but it could have been a third season damnit! I guess I am just sad that one of the best anime I have ever seen ended in less than 30 episodes =(
One more thing I have to add: JoshV mentioned the animation being superb and I cannot reinforce that enough. The action sequences in season 2 are more fluid than they are in season 1, and they are beautiful in season 1.
I guess I will just stop beating around the bush. Add this anime to your list as soon as you can and watch both seasons in one sitting. I guarantee you that you will not be disappointed. If you don't like it, uhh... Daystar will give you a backrub!