Well, that depends. Try this handy checklist:
Do you want your rug to stay put (no creeping, wrinkling, or sliding)?
Do you want to have a nice, soft cushion for your feet (or knees and tush if you’re crawling around on the floor)?
Do you want to protect your floor from getting scratched by the backside of the rug and any dirt that makes its way in between the two?
Do you want to lengthen the lifetime of your rug by protecting it from stretching?
If you answered yes to any of these questions, you need a rug pad. I’ve tried various pads from West Elm, Ethan Allen, Karastan, and a random Amazon seller. My favorite by far is Karastan’s Down Under Rug Pad and you’ll never guess where I found them for sale the other day. Target! Yessssss!!!!! The Down Under pads are nice and thick with a rougher side on top to grip the rug and a cushy side on bottom to keep things from moving around on the floor. (By the way, the thin mesh rug pads that exist out there? I've tried them, too. They never manage to do what they're supposed to.)
When you're ordering your rug pad, make sure to get as close to your rug size as possible without going smaller than the rug. For example, the rug in the picture above is 5'9" x 9'. I got a 6' x 9' rug pad and cut it to size with a sturdy pair of utility scissors. Your rug pad should be about 1/2" to 1" smaller than your rug all the way around. (I also trimmed the corners so they didn't show under the rug.)
**A word of caution—if you’re allergic to latex you’ll need to pay special attention to the content of the rug pad you choose.**
One last thing to keep in mind about your rug. Rugs shed. Quite a bit, in fact. It's absolutely normal and can last up to a year. All you need to do is vacuum it regularly, which you should be doing anyway.