Both provide key-value access to data. The Hashtable is one of the original collection classes in Java. HashMap is part of the new Collections Framework, added with Java 2, v1.2.
The key difference between the two is that access to the Hashtable is synchronized on the table while access to the HashMap isn't. You can add it, but it isn't there by default.
Another difference is that iterator in the HashMap is fail-safe while the enumerator for the Hashtable isn't. If you change the map while iterating, you'll know.