Google is a puzzle for many of us, but until we find the last pieces, let's try Wei-Hwa's Puzzle Challenges, a module for Google Personalized Homepage with really tough puzzles. Perhaps because the puzzles are created (or at least carefully selected) by a Googler.
You can also participate to Google U.S. Puzzle Championship. The registration is open until June 15. Here's the test from 2005.
Related:
The brilliant Niniane Wang
Google Calculator
Googler's list