Yes, Ninjas can become invisible. Most of the time it was a great trick. Illusions that made the opponent think the Ninja disappeared, while he actually was somewhere hidden or ran away. The Sensei taught us some tricks of disappearing using shuriken, but its hard to explain it writing.
Then there were other methods of esotheric practices of the mikkyo Ninjutsu which made the ninja 'disappear'. This is even harder to explain, however, I won't even try to explain because I shouldn't be even talking about it ^^;