Do any stars exist apart from galaxies? Do any stars exist apart from galaxies? Do "maverick" stars exist?
 A: Yes, as this link (suggested by Will) shows.  They're expected to basically always be stars that used to be in galaxies (they formed there), but have gotten kicked out somehow.  You won't really see many stars forming between galaxies because there just isn't enough matter there to collect into stars.  Even the ones you do find will be in messy regions fairly close to other galaxies.  The most common way for the kicks to happen is if three stars (or two stars and a black hole, or something like that) get together, one couple can give an enormous boost to the third.
But the speeds you need to really fully escape are enormous.  It's easy to get kicked out of a little cluster, but you might still be stuck in the galaxy itself.  To get all the way out, you would typically need speeds of thousands of kilometers per second.  And that kind of speed is unusual for simple stars, because they tend to break up if they're hit with too much force.  We know of one way it could happen with black holes, though.
