It depends. You need to make sure that the electrical specs are the same. For example, the adapter I have for a 13" MacBook Pro is 16.5V @ 3.65A. If both adapters are identical in the voltage and amperage, then there shouldn't be a problem. If either of those are different, then you will run the risk of damaging things.
Is there any reason NOT to use the powerbrick from my earlier MacBook Pro with the new one? I know the new brick is bigger and more powerful (85W) but will anything go wrong if I use the old one when I plug in at my office?
How about a 60W brick for an old MacBook?