Funniest moment when catching a Pokemon.

It was quite interesting actually. When I was trying to catch a Murkrow it took me hours to try to find one in Pokémon Diamond/Pearl. I finally found one and I was happy about it but then my friend jinx me saying "Watch your going to be down with your pokeballs and you would have to run all the way to the Pokémon center to buy more Pokeballs" well guess what happened? I ended up using up all my pokeballs and having to go to the Pokémon center. It was quite funny even though I raged over it haha.

 

Oh god. My playthrough of Silver. (This bit was actually done in our form room time at school, where we had an hour to chat before the Christmas assembly.) I finally found Lugia, and I'd come prepared with tonnes of Ultra Balls. But, in regular legendary fasion, every single one failed. I even had it Paralyzed and on 1 HP! Then finally, I ran completely out of Ultra Balls, and I had to resort to the "Leftover Balls", you know the ones, Poké Balls, Net Balls, all the ones I never used. And then, I finally got whittled down to my last Pokéball. Just a standard Pokéball. I turned to my friend, and said. "Well, this is the last one. At least I've saved, I guess." And we both watched as my last Pokéball flew through the air, an proceeded to wobble... and another wobble... Wait, another wobble? Could it be...?
*Click*
At that moment, I proceeded to cheer very, very loudly (Much to the dismay of the class!), and my friend just sat there, stunned. Pretty soon we both burst out laughing. One of the best moments I've ever had with any Pokémon game ever!

(Yes, it is uncannily similar to your story, @[member="sohrob101"] )

 

So recently, I was fishing for a Carvanha and pulling my hair out because I couldn't find one, and managed to reel in a Feebas before I found the much more common shark Pokémon. I was like "This is cool, but definitely not what I was looking for." *tosses Feebas back*

In another encounter with Mesprit in the Nameless Cavern, I was freaking out because I was running really low on balls after previously encountering Groudon and Cresselia and it kept breaking out of all my Ultra Balls. So of course I caught it in a Poké Ball.

 

I just remember that whenever I first encountered Articuno, back in Fire Red, I was throwing great ball after great ball, until catching on ball 30. This was pretty cool, an exact even number, as well as the fact that it was my last great ball that caught it.

However, when playing HGSS, I encountered Articuno again, and this time caught it with an Ultra Ball. The 30th ultra ball. It wasn't the last, but the fact that I caught it on ball 30 entertained me, because it was a pretty awesome coincidence.

 

Hmm, I've got a few...

There was that time the first ball I threw at Yveltal was a critical capture, for one.

And while not mine, my friend recently caught ORAS Groudon in a Nest Ball while we were Skyping, which led to an excessive amount of loudness and my parents yelling at me.

But I think the best one is probably how in both Black and Black 2, I could NEVER catch Virizion. EVER. Seriously, it would Struggle-suicide before I could catch it, and that happened on multiple occasions. < So along comes one of friends, I tell her about the problem, and she catches them on the fourth or fifth Luxury Ball.
ASDFGHJKLJDBFAKJBFLAJDB

 

That moment when I caught my Virizion inside of a Net Ball. I didn't throw the Net Ball on purpose and it... well.. caught the Virizion. I was so surprised that I ran out of the room.