I will be traveling to Greece this September together with my fiance. We want to catch as much of the Greek spirit as possible, that's why we will be traveling most of the time by train. We will be heading to Greece from Romania. Though we established an itinerary, we haven't made any reservations because we don't know how much time we will be spending in each place and we heard that it is better to have a look at a hotel room before paying for it.
My question is: are there any requirements at entering Greece such as a certain amount of money, an invitation from a Greek citizen or hotel reservations? I need to mention that I am an American citizen and my fiance is Romanian. Thank you in advance!

As an American citizen there are no requirements put on you in advance of entry. I don't know about an Romanian passport holder, but my guess is that the situation will be the same for you both.

Your finace needs to contact his embassy or consulate to find out what the rules are - frequently they are different for citizens of some central european countries.

Snow:

you'd rather visit http://www.mfa.gr/english/foreign_po.../visa_inf.html

this is the official site of the greek foreign office. It seems that there are no special requirements neither for you nor nor your fiance other than being able to produce a valid passport.

Thank you for your replies and the information provided. It seems that I won't have to show anything but the passport but my fiancé will have to provide the proof of 100 euros/day during the stay in Schengen area( I believe it's just a Romanian regulation). We are lucky because they want to impose the invitation and reservation requirements starting Oct,1.
By the way, did anybody enter Greece by train? I am just curious how is the Customs in this case. Thanks!