Here are pictures of the cozies I did make. They were all pretty easy to crochet. I used cotton yarn (Sugar and Cream).
Really simple coffee sleeve with flower in single crochet - use a cozy instead of the cardboard sleeve available at coffee stands. These cozies are small enough that you could carry one in your bag or tote. I do like bright pink. Think I will make one for myself! ;')
Another is a cup cozy that fits a standard coffee cup crocheted with a half double crochet stitch. I like to make the bands somewhat narrow so the edges do not touch the bottom or top of the cup. This eliminates tipping the cup or getting lipstick on the top edge. Also, who wants to taste yarn with their coffee or hot chocolate??
A third cozie is one which fits the whole cup. The sides and bottom are crocheted in single crochet. The bottom acts as a coaster.
Here are a few websites with free cozy patterns:
Martha Stewart Crafts
All Crafts (has pictures and patterns for over 100 different cozies)
Crochet Pattern Central (many different types of cozies)
If you do not have the time to crochet a cozy, you can purchase one or more at my Etsy shop (http://www.etsy.com/shop/CraftyPastimes) .