Heroes is probably my favorite show on television and I can't wait until the start of the spinoff season, Heroes: Origins.
I think the show is incredibly creative and Noah Bennett, Hiro, and Sylar are probably the best characters out of the entire thing for me personally. Especially Sylar...he's a truly disturbing bad guy and the way that he absorbs the powers of others, while it's never really shown, is pretty disgusting.
But like Stone said, they definitely don't just wake up with the powers one day. I think even Claire had shown the ability to heal herself way before the first taping of her jumping off the water tower and breaking her own bones, but I could be wrong.
And I've never seen Wild Cards, but I do know a bit about it to know that other than the superhero tie-in, I couldn't really think of any other blatantly obvious similarities between the two.