One possibility is that there's not enough free internal storage on the phone. Another is that the carrier is having problems. Or the sender's carrier is having problems. (Does it happen only from people sending from one carrier or from people sending from different carriers? That will localize that one.) If it's your carrier, go to their store and see what's happening. (Their MMS server may be down.)
Another possibility is that the sender's carrier allows larger attachments than yours does, and your carrier can't handle those larger attachments.
(This is a "you have a symptom - you have to determine the problem causing it" situation.)