What makes ancient Greece so special?

Well, for ancient Greeks, their language affects ours, as a good portion of English Words have Greek roots or are just plain Greek. They were a powerful culture, affected others strongly, like Roman, whose language also affects ours. Parts of their culture are entwined with ours, like Cupid, the Greek god of love. The hearts for Valentine's are his arrowheads. There's thousands of other things, like constellations.

Also, a good portion of Biblical stories are derived from Greek stories.

Plus, their religion is interesting.