If you have a favorite yoga mat, you can fold it to fit in your bag. However, regular yoga mats can be bulky and heavy, so you might want to consider getting a special yoga mat (or yoga towel or sling) designed for traveling.
My favorite yoga mat for travel is the eKO SuperLite® Travel Mat by Manduka. It weighs about two pounds and folds up easily. It’s grippy on both sides, and it’s rugged enough to be stable even on plush carpet.
The Lululemon Un Mat is comparable to the Manduka eKO SuperLite®. An affordable option is the Gaiam Travel mat, which is reversible, with an absorbent side handy for sweaty vinyasa classes, and weighs only one pound.
The Yogitoes Skidless towel has little grippy bumps on the bottom so it won’t slip around on the floor or on top of a regular yoga mat. They are available in lots of fun colors, weigh only 1.25 pounds, and are also really durable.
A plain microfiber towel like the Manduka eQua, which weighs only one pound, can double as a beach towel or picnic blanket.
I use a lightweight day pack and put my folded mat in it if I’m visiting a yoga studio on the road, but a mat sling like this one from Gaiam for toting your mat doesn’t take up much room if you prefer to roll it once you’re at your destination.