The first Olympic Games in history took place in Olympia, which tells you the cultural and historic importance of the place. Visiting the remnants of the ancient city was one of the intense moments of mytrip to Greece and I saw a number of really impressive things there.
The Temple of Zeus is one of my must-see places. Colossal and with beautiful ruins still remaining, as the temple's two pediments (sculpted with mythological scenes) prove. The temple contained the famous chryselephantine statue of Zeus, one of the Seven Wonders of the Ancient World. Unfortunately there's nothing of it left.
I was also able to see a temple dedicated to Hera, the best preserved building in Olympia, the site of the Olympic stadium and the remnants of the gymnasium (only the foundations remain, but the surface area is impressive).