I don't know if anyone mentioned this or not, but in the anime there's an episode where some penguins invade and Escargon remarks that they look like Dedede.
Now I don't know if any of you watch the anime or not, but Dedede and Escargon are always together. However, Dedede was knocked unconscious RIGHT before he says his DDD comment. When Escargon realizes DDD is unconscious, he tries to wake him up, saying his relatives are here. I'm thinking the writers kept Dedede unconscious on purpose to keep Dedede from remarking one way or the other about his relation to penguins.
And when Dedede finally does see the penguins for himself, he doesn't say anything either way about their appearance and his. Neither do the penguins.
The official answer, I believe, is that Dedede is just some made up fat thing, mostly evidenced by the fact that he has hands, not wings. I, however, will continue to think of him as a penguin. For one, penguins in cartoons/games are always blue (or black). Second he has his funky feet that make him look like he waddles, which penguins do. And third the beak, while it doesn't look like either a duck beak or a penguin beak, gives away that he must be some kind of bird.
He's definitely NOT an eagle though.