There are loads of different varieties of paradox, some are semantic, some are logical and some seem to unravel* the nature of reality itself.
Granted, most paradoxes are dreamt up by bored philosophers that definitely need to get a hobby, and probably aren't going to serve you all that much in your day to day life, but they certainly give the rest of us something to think about when we're on the train/at work/lying awake staring emptily into dark space for the fifth night on the bounce (just me?).
Aside from bored philosophers, it's becoming apparent that, if we were to solvesome paradoxes (hint: it rhymes with lime gravel), we could be on the cusp of some major scientific breakthroughs.
So, get ready, warm up that brain and take your shirt off, because we're about to do some naked mud wrestling with the very concepts of Logic and Reason (and something tells me that Logic and Reason are going to win).
*Incidentally, does anyone else think that it's paradoxical that you can "unravel" something, but not "ravel" it?