I think there is another topic where the question "when did they fall in of love with each other" is already debated.. Admin could maybe tell us which one it is.. 

by the way it's an interesting question and the answer is also interesting but I think we don't really know..

I have no idea when it is they may have realized they loved each other, but IMO, the moment when they realized they were heading in that direction was at the end of When the Bough Breaks, when Beckett thanks Castle for his help with the case.  Then they say their goodbyes because she thinks Castle is heading off to write books for "a certain British secret agent".  Castle gives her the cutest puppy dog look and they shake hands. Then there's a moment when Beckett looks deep into his eyes and you can tell she doesn't want him to leave and he feels the same.  I saw that for the first time and yelled "Kiss her already!" at the screen.  Then they head off to another crime scene bickering and I said to myself "Those two are crazy about each other."