There is no specific rule on what size yoga mat you should use. But there are a couple of things to consider:
To stay secure (not slip) in a pose, your hands and feet should be on the mat in such poses as Downward Dog. To start in this pose your hands are at chest-level and your legs are straight.
You might also want to consider a mat that is long enough so that when you are lying on the floor your face or head would also be on the mat and not on the bare floor. This could be for several reasons: to keep your head off of a cold floor, for cushioning, or just for personal comfort when in a public studio.
A longer mat would allow for you to perform flow poses more easily by not having to continuously reposition yourself to stay on the mat.
Buying a mat longer than you need, however, will just mean more weight to carry and more bulk to store.
The standard length yoga mat is 68". You can also find yoga mats that are 72 or 74 inches long. We've recently added extra-long mats for yoga or Pilates that measure 84".