Be Nice to Your Hair Tip #1: Toss the Terry Cloth

Treat your hair like a cashmere sweater.  If you read posts about hair, you see this statement over and over.  It is a bit of a cliche, but it is true.  Once you damage your cashmere sweater, the damage is there forever.  This is also true of your hair.  Would you rub your sweater vigorously with a terry cloth towel to dry it?  No way.  You shouldn't do this to your hair either.  Terry cloth is a very rough fabric and rubbing your hair with it will rough up the hair's cuticle (see The Structure of Hair) and cause permanent damage. This is true for all hair, straight or curly.
First off, don't rub your hair to dry it.  Squeeze or press out the water.  Rubbing is unnecessarily damaging.
Secondly, use a fabric that is gentler then terry cloth.  Here are some options:

Microfiber towels-  You can use microfiber towels from the automotive section or you might find microfiber towels marketed for cleaning.  You can also get microfiber towels made for hair.  The brand name of mine is Aquis.  Turbie Twist makes a microfiber version of their hair turban.
Flour Sack Towels- found in the kitchen towel section of stores.
100% cotton t-shirts-  It is a good use for your old 100% shirts.  Some people find long sleeve t-shirts work best for plopping (see below).

If you have curly or wavy hair, you you may want to scrunch your hair to a damp state with one of the options above.  For some people (like me), scrunching breaks the curls into smaller curls and/or causes frizz.    Another option is to Plop.  Plopping is accordion folding your hair upside down onto a non terry cloth towel and then wrapping the hair up with the towel.   Here is a good video.  They call plopping plunking in the video.  If you want more videos, do a search for "plop hair" on youtube.com.  You will come up with several videos.
Jessicurl's plopping (A.K.A. plunking) video
As they say in the video, 20 minutes is a good amount of time to plop.  People have luck with longer or shorter plopping times.  I find at some point the microfiber towel has pulled out all the water it can from my hair.  At this point the damp towel is keeping my hair wet, rather then making it dryer.  I take off the towel at this point.  You have to experiment to see what plopping time works best for you.  For some curlies and wavies, plopping simply doesn't work because it causes frizz. You also may want to experiment with types of towels.  For example, some people find microfiber to cause frizz, but flour sack towels don't.
You have to keep trying things to find out what works for your hair.
Remember, if you are nice to your hair, it will be nice to you.