When my daughter was two, I thought she was ready to try the game Memory. I looked at the selection in stores, and every version was plastered with some TV character she didn't know. I thought to myself, "They're just cards with pictures on one side. I can make that!" I happened to have some mat board scraps in the back of a closet that would eventually end up in the recycling bin anyway, so I cut those into rectangles to use as a nice, sturdy card.* I scoured the internet for some free clip art that would appeal to my daughter, copy-and-pasted them into a Word document, and printed them out.** I cut them to fit my mat cards and used double-stick tape (the ultra-flat scrapbooking kind) to attach them. If you use wet glue, it could wrinkle the paper.
They've been very well used over the last 3 years, and now are getting a second round with my son. I just love them...and such an easy project!
*Not many people have extra mat board laying around the house. Any heavy cardstock will do. You certainly don't have to buy anything special, just dig around in your recycling bin. Empty cereal boxes, old greeting cards, etc. While the mat board is super thick and can withstand a little toddler drool, it also requires a heavy duty utility knife to cut it. (Don't forget to put something sturdy under it so you don't cut up your floor or coffee table!) Using a thinner material, like cereal boxes, will be much easier to cut, but won't last as long. This can be a good thing, because when they wear out, you can just whip up a new batch with updated pictures for your little one.
**Use any images you like, just make sure you have two of each image, so your child can make pairs. This would be a fun thing to do with family photos!