"Q. What is this?
A. A challenge to confirm whether or not a professional, established data recovery firm can recover data from a hard drive that has been overwritten with zeros once. We used the 32 year-old Unix dd command using /dev/zero as input to overwrite the drive. [...]"
It's been over a year, and nobody has accepted the challenge yet. Even if there isn't any prize money to win, I'd think that the PR opportunity would be quite enough for any data recovery firm to do it.
So my conclusion is: overwriting once is plenty good enough. You want to overwrite the whole disk though, otherwise the filesystem might leave metadata clues even after the file has been overwritten and unlinked.