My favorite character encounter was in May 2000. We were at MK at opening, waiting for the rope to drop at the castle, so we could make our mad dash to the Pooh ride (it didnt' have a fast pass yet, so we wanted to ride it first before the crowds). There was only one group ahead of us when we arrived there, and as the hunny pot rolled around, Pooh was on it. We were so jealous for a split second, because we missed riding with Pooh by one ride. But the next pot came and Piglet was riding, and we were able to ride with Piglet! My girls were 9 and 5 at the time, and my son was 2. It was our very first ride at WDW on our first trip, and it couldn't have been more magical! When the ride was over, we got to walk with Pooh and Piglet to their meet and greet area, which at the time was right in front of the former lagoon, and I have the cutest picture of my 2 year old walking hand in hand with Piglet.
My other favorite encounter was in June 2004 at AK, with Goofy. We were next in line when he had a 5 min break, and he came back with his zipper down on his fishing pants. My kids thought this was hilarious and gave him a hard time, and the whole line was cracking up. It was great!