The GCJ was google's spin off from the standard TopCoder algorithm competitions (see http://topcoder.com/tc). In fact the first two GCJs were run by TopCoder before Google decided they wanted to run it themselves. I suspect the Hacker Cup is also being run by TopCoder.

GCJ is itself similar to the much older ACM's ICPC ( http://cm.baylor.edu/welcome.icpc , around in some form since 1977 http://cm.baylor.edu/ICPCWiki/Wiki.jsp?page=The%20Early%20Ye... ), though of course it's not limited to college students.

The ICPC is fairly different in format though. For one, it's always team-based, and usually has much harder problems since the entrants are always university-level students who have taken advanced algorithms courses. I've participated in both TopCoder contests and the ICPC and the GCJ/HackerCup are definitely TopCoder-style rather than ICPC.

Based on their engineering puzzles[1], I'd maybe expect problems geared more towards approximation/heuristics. The GCJ problems always require exact answers.

[1] http://www.facebook.com/careers/puzzles.php

So? More money (or free tshirts) for idle programmers I say :D