It depends on where you get them.
Directly from the military they're probably made a while ago and have 2-3 years of shelf life on em.
If they're MRE's made for civilians, they can last up to 10 years.
Are there any numbers at all on them?
You can also tell by the name. Some of the wording or the flavors themselves did not appear until certain dates.
Storage temperature plays a big role in how long they last. Unless the bag's punctured, its still edible past the expiration date but it'll just taste horrible. According to these guys, the storage lives given are for when they no longer taste good, not for when they can't be eaten anymore.
My neighbor left me a box of MRE's post Y2K and they were about 8 years old, tasted great.