I If you defend early using hoplites, expand (courthouse helps), and build alot of cities your bound to be powerful.
Well first off I'd just like to point out that this is true of any civ and isn't specific to the greeks (besides the hoplite part).
As for how to best use the greeks, I'm not sure. I've only played one or 2 games with them myself so far. I think you have to decide if you want to fight an early war or not though. Starting out with democracy is pretty nice to get a head start on early teching, but it prevents you from going to war. While you can drop out of democracy, declare war, then go back, in the early game, I've found the AI is more likely to offer peace (on emperor, maybe not on diety?), thus making it hard to stay in a prolonged war as a democracy.
Therefore, I think the best way to play the greeks might be defensively at first, and using your increased science from democracy to get a tech lead (researching defensive techs and ones to help increase your science rate). Once you've set up a solid start, and have at least 3-4 good cities running and you get a solid lead in techs, you can start looking into fighting a war (for example, if your the first to mathematics and catapults, or metallurgy and cannons are both times to build a quick couple armies and take a few cities from a pesky neighbour).
Of course, if you manage to set up a solid empire of 5-6 cities without any wars, you can always settle down to the defensive, and either go for a tech win or cultural victory (due to the increased numbers of great people).
I'm sure other people who have played the greeks more then I have will have better advice/strategies to offer you, but it seems to me that the greeks are very flexible if you can leverage that early tech lead having democracy from the get go offers you.
