I like to think that it happened gradually, that there was not one moment where a switch was flicked somewhere and they fell in love. I think it happened with time, and neither Castle nor Beckett realized that.

Of course, there's also a moment of realization, a "aha" moment where they realized they're in love with each other. I think Castle's was in "Poof, you're Dead". And Beckett's was probably in 2x24. Then she bottled it all up and tried to fight it, in season 3. But deep down, she knows she's in love with him.

But yeah, I don't think there was a moment where they fell in love. I think it happened progressively, without them realizing it. The process of falling in love and the moment they realized they're in love are two different things.

Agree as well.

As to the aha moments (had some fun looking for them).
Castle throwing his hand at poker with Beckett during season 1.
Beckett reading the dedication to her at the first Nicky Heat novel presentation.

This may seem a little early in the series, but I think that Beckett fell in love with him at the end of 02x01 when he came back after his talk with Alexis and simply said "I'm sorry" for getting involved in her mother's murder.  After she says, "Castle, I'll see you tomorrow", I envision her sitting at her desk and emotionally exhaling and saying to herself, "Damn, what am I feeling here?"

As for Castle, that is a little harder to decide.  Despite all the insistent flirting and watching Sorenson, Demming, and DMB go by, it was probably later on, not till season 3.  I might be missing something, but I don't think he realized it was love until Martha asked him to be honest about the reasons why he is still following her. (Was that Knockdown?) And in that episode, when she asks him "Why do you keep coming back?" and he stutters and is all flustered– that realization carries forward into the kiss and the subsequent pounding of Lockwood. 

I might be in the minority here but I'm convinced Beckett fell far earlier and as I compare seasons 1-3, there is a flip-flop in who is the catalyst.  Season 1–Castle.  Season 2–Beckett.  Season 3–Castle.  What will season 4 bring?  If they follow the pattern then I predict that Beckett will be the driver and catalyst for the emotional moments.

Just .02

I think Beckett had a crush on Castle from the beginning, even before she actually meet him. But it was something that you feel for someone that you admire, she felt that for Castle the writer, but she is in love for Castle the man during 2nd season.

I agree that they have been slowly falling in love for 3 years.  I don't know when it changed from attraction to true love, but I have an idea of when each of them had that Aha! moment where they couldn't deny it to themselves anymore.

For Castle, I think it was in Poof!

For Kate – LA, definitely. 

Just my opinion. 

I also think they have been falling in love for the past 3 years already, the moments of realization are hard to determine.

Altho I think Kate realized her feelings for the first time during the season finale of season 2 (and got her heart broken in the process) I really think the moment of true realization about how much he means to her was during "To Love and Die in LA", after she read Royce's letter in the airplane. The look in her eyes when she looks over at (sleeping) Castle said so much and spoke for itself. She finally came to terms with her feelings.

and with Castle… I think it's hard to say. He's clearly been smitten with her since day 1 tho.