Thanks everybody for prompt responses! I guess my nerves are now playing a horrible tricks with me - just this is the first time (and I pray to God the last time) my wallet was stolen.
Here is the sad story: I was warned by a friend of mine that there are a lot of theft going on in Athens (I went there for his wedding).
So I was 'extra' careful' - got a small lady bag with a long handle (so that I can put it diagonally over my head and keep it always in front of me).
I had kept my hand *always* on top of it (most photos I have from Greece will prove this Everything was fine and I visited many places and was quite happy about my Greek experience. Then I went to Syntagma square (in front of Parliament buildings) - it was about 20.55. And then I made a mistake. I saw that it is only about 5mins until change of guards and I decided to go and see it once more (was not too happy about the pictures I made earlier that day).
So I was there, taking few photos (lasted only 1-2 minutes) - this was the only time during the day I have taken my hand off the bloody bag!
When it was all done started to make my way to metro. And then I noticed that my bag is too light (I mean beside mobile and wallet there was nothing else in it!)
My bag was closed as usual but I opened it and the wallet was gone

So the buggers have opened the bag, grab the wallet and closed it! Professionals, no doubt about it!
The rest is just a whirl of trying to find the police station to report the theft, going back to hotel and explaining that my room card was also in the wallet, etc…
Btw. In the police station they tried to convince me to say that the wallet was lost (not stolen!) so that they can issue me a certificate right away and case closed.
I refused to say that (the bloody thing was stolen not lost - grrr...

so they told me to come in about a week to pick up the paper. They will not post it to you!
Somehow I manage to name my friends father as a person who will come to pick it up - so I hope in a few weeks I will have the certificate in my hands.
And I was told I was lucky - if they had stolen my passport - I would have to wait for three months! What the hell would I do in Greece for three months without passport? As I am a non-EU citizen, it is not that easy to move around WITH the passport and all visas in order. I hate to think what would I be facing without the passport. Ah well …
@kitkat64: yes, definitely do not bring nothing unnecessary with you while out and about - keep valuables in a hotel safe! Few euros and photocopy of your passport should do the trick when strolling around. I normally do that when I am traveling but this time the circumstances were not your usual traveling-for-fun and I got busted

Again thanks a lot for sharing your unfortunate experiences and tips with me.
Ema