Does anyone have experience how to get downtown from the airport? Is there a bus, train, subway service? We are staying at the CP.

There are most of the above! Metro, bus, suburban train and taxis:
http://www.aia.gr/pages.asp?pageID=981&langID=2

Depending on what time of day you arrive and how much luggage you have, there are 3 real options:
1. Subway.. Metro.. clean, fast, cost is 16 euro per person one way but you have to schlep your luggage around alot.
2. Taxi.. fast, no schlepping of luggage, will cost about 40-50 euros during the day, more at night.
3. Bus.. a little schlepping.. cost is 4.50 euro one way. express buses go frequently from airport to all central locations in Athens.

Super, since we only have carry on, "schlepping" will not be a problem. Leaning towards the bus service then. Thanks for your replies!

I think he or she means 6 euro per person each way.

That sounds very expensive to me. Unless you hit an incredible traffic jam, you should have change from 30.

The CP website indicates that the airport is about 29 km from the airport, for a 35 minute ride. They claim the taxi charge to be 25 euro. I feel, that
would be quite low and unrealistic, especially compared to London or Paris. Also, I am never comfortable with taxis from an airport to any destination that I have yet to experience, because one does not have a reference point yet. I remember how I got screwed in Bangkok the first times until I had things under control. I know nothing about Athens, so maybe I feel more inclined to use the bus or the subway. Also I don't speak Greek and I have no idea how their English speaking abilities are. That's always a good reason for taxi drivers to cheat or at least try to. By the way,are the signs in Greek and in Western characters as well?

I never take a taxi from the Athens airport. Too many people I know have a horror story to tell. And we're Greek. I'm not a confrontational person and I don't want to be stressed out thinking about what might happen.

Your hotel is near a subway line, so I would consider that. Signs are also in English.

I know exactly how you feel. I am Swiss and have similar experiences back home as well as in other German and French speaking countries, that is too say that even speaking the native language is no guarantee for honest service. Not speaking the language multiplies the "getting screwed" chances by a huge factor. Taxi service from any airport is sort of shady by nature, it seems, so I am quite apprehensive about this.

Taxis in Greece are very cheap, unlike pretty much everything else you'll be buying here (in the last week I've been staying in SKG, I 've paid, inter alia, 1.18 Euros for a 50g bag of potato-snacks from the supermarket and no less than 5 Yuris for a cappuccino at a downtown cafe- I've heard about some place in ATH where a coffee costs SEVEN!).
London and Paris are the most expensive cities in Europe if not the world, so the comparison is rather pointless to begin with. A similar ride in Madrid would probably cost around 35.

Taxi drivers will sometimes try to cheat you, but, knowing the approximate fare that you should be paying, it's easy to figure whether they are doing so. They have to give you a receipt so do ask for one if you're in any doubt. Pretty much everyone in Greece speaks a bit of English, so you won't have a problem getting them to understand where you're going.

Having said all that, I see no reason to take a taxi unless you have a lot of luggage with you. The Metro/Proastiakos combination is both faster and cheaper!