I replied to FReeper Son-Joshua's post that I'd lean toward Goliath being Anakim more than Nephalim (Gath was the home of the Anakim). But in truth we're not sure because the 1st Samuel text doesn't say why he was a giant.
But as far as Nephilim after the flood goes, it's possible. Think about it. Who exactly was on the ark and exactly which ones do we have the info on their ancestry?
Answer: We have no info for the ancestry of the wives of Noah and his sons. So it's entirely possible that the genes from the Nephilim or anyone else were passed on through the wives. It's also possible there were some recessive genes going on (i.e. Japheth's wife and Ham's wife might have been normal size or whatever even though they may have been carrying some recessive genes of the Nephilim or from anyone else. Likewise, with Noah's wife, or for that matter one of the men might have had a recessive gene.)
Making the destruction of humanity and Earth by the Deluge a moot point. That’s a pretty big oopsie, but I guess God would be up to it. If God made oopsies.