In Greece, there’re three carriers, Cosmote (coverage map), Vodafone (coverage map) and Wind (coverage map). The standard Internet access charge is 1 € per day (at all three carriers), plus the cost of the SIM card.
Foreigners can buy SIM cards in local stores, just bring your passport or ID. Be aware that many shops prefer to sell you more expensive bundles (e.g. with 3G USB sticks) stating they ran out of stock of naked prepaid SIM cards.
I went for a 20 € KartoInternet pack from a local Vodafone Store that includes 10 days of Internet access (so the SIM card runs at 10 €). The card is valid for 12 months after the last refill. It comes in standard SIM format. If you plan to use it in an iPhone 4 or iPad, cut it down to Micro SIM format (either manually, or using a Micro SIM cutter).
The maximum data volume for the 10 days is 3 GB. Check the online status page (link only working when logged on) to see how much data volume you’ve left. To fill up the account, you can purchase top-up vouchers in many supermarkets (they don’t offer the SIM cards!).
APN: web.session (blank username and password)