Yes they do, but they require cleaning. There are pro's and con's with both types.
But you did not answer the question; which do you use?

I use both kinds. With plastic cards I find that I need to clean them about every 5 or 6 games. Paper cards I open a fresh deck every game. I only use Bee or Bicycle brand paper cards. Mostly I use paper but I do enjoy busting out the plastic once in a while. - bluegaragepoker 5/1/2012