Coasters are such an under appreciated gift, especially if the receiving party can get to participate in the decoration process.
As a nice house gift, I made my girlfriend and her three roommates a set of coasters, (in the shape of her favorite animal), that they could decorate to their own liking. I don't normally let other people in on my projects, so this allowed me to share the joy and pride of making something and being able to actually use it.
1/8" hardwood board (oak looks nice)
acrylic or oil paint (for the decoration)
polyurethane (for the waterproof finish)
Total cost is about $8 if you just buy the wood and have the rest of the materials handy.
Step 1: Find a picture
A quick Google search does the trick, then off to scale in Word, and then cut out the picture.
The coasters can be any shape really, as long as they're bigger than the diameter of the average coffee cup, which is about 3-1/4", so any shape longer than 3-1/2" both ways will work.