I just did a regular format on a virtual 10MB drive with Vista, and it did zero it. The quick format did not; the test data I copied onto it was still visible and recoverable. That could be either good or bad.
For a brand new drive, there is no point in zeroing it. If you want to check it for errors, there are better ways, as Molly suggests. So do the quick format.
Reasonable people may disagree as to the non-tinfoil-hat feasibility of recovering data that has been simply zeroed, as opposed to overwritten 35 times with random patterns first. Surely the latter is not worse security-wise; but the former may be sufficient, and definitely takes much less time.