As others have said, timestamps can represent a smaller range of datetimes (from 1970 to 2038). However, timestamps measure the number of seconds since the Unix Epoch (1970-01-01 00:00:00 UTC), thereby making them independent of time zone, whereas DATETIME stores a date and time without a time zone. In other words, timestamps unambiguously reference a particular point in time, whereas the exact point in time a DATETIME refers to requires a time zone (which is not stored in a DATETIME field). To see why this can matter, consider what happens if we change our time zone.
Let's say we want to store the datetime 2010-03-27 12:00 UTC. If we store this and retrieve it using a timestamp or DATETIME, then there usually appears to be no difference. However, if the server now changes so that the local time zone is UTC+01, then we get two different results if we pull out the datetime.
If we'd set the field to a DATETIME, it would report the datetime as 2010-03-27 12:00, despite the change in time zone. If we'd set the field to a timestamp, the date would be reported as 2010-03-27 11:00. This isn't a problem with either datatype -- it's just a result of the fact that they store slightly different information.