I have really thick hair, and my shower drain tends to clog fairly frequently. It's always best to keep it clean regularly, before it becomes a problem (unfortunately, I speak from experience on this). I used to struggle with bent wire clothes hangers, fancy plastic tools designed for cleaning out showers, plungers, and Liquid Plumr, but in my experience, none of these work as well as a thin barber's comb.
That's right! Remove the drain stop (or even work around it if yours doesn't easily come off), then use the skinny end to grab the clumps of hair (and slimy stuff) and pull it out.
See? Yuck. But it works great. Be sure to dispose of the gross stuff in either the toilet or trash can - don't just wash it down the shower drain (again, I speak from experience).