There's almost no mutual intelligibility, in my experience. Probably a little bit less than between English and Old English. Some words will sort of look the same on paper, but the pronunciation is completely different and there's plenty of new loanwords that didn't exist in the ancient language.

After learning Ancient Greek for 5 years, Modern Greek sounds like gibberish to me. And I know from my experiences travelling in Greece that Ancient Greek sounds equally like gibberish to modern speakers.

That being said, I have been told that knowing Ancient Greek (especially from the Hellenistic texts) makes learning how to READ Modern Greek a lot easier, since the Greek spelling system is rather conservative. The problem is that the modern spelling system, as was mentioned above, does not reflect the actual modern pronunciation.