Most places in Greece have Western-style toilets, especially hotels and restaurants that cater to tourists. You'll occasionally come across Asian-style squat toilets in older houses, kafeneia (coffee houses) and public toilets.
Public toilets are a rarity, except at airports and bus and train stations. Cafes are the best option if you get caught short, but you'll be expected to buy something for the privilege.
The Greek plumbing system can't handle toilet paper; apparently the pipes are too narrow and anything larger than a postage stamp seems to cause a problem. Toilet paper etc should be placed in the small bin provided next to every toilet.