So far, Dropbox has never corrupted anything. I don't think I've ever heard of it corrupting someone's files, either.
Plus, factor in the fact that Dropbox keeps backups of all your files, so in the worst case, I'm guessing they can restore anything that breaks.
Put that against the fact that not using Dropbox means I'm trusting my hard disk not to die on me, and I think Dropbox comes out ahead by far.
Do you know of any reason I should be more worried?