I don't have a definite favorite moment. I remember them all the same and all were very entertaining. This is mostly in time-order:
1. Playing the game Pharaoh on PC for months on end. I would get a kick out of trying to make my city as best as it could be. I even eventually started making Pyramids, but I never got to finish a very large one. It takes WAY too long, even for the hours per day I was playing!
2. Diablo 2 must be one of my most played games of all time. I loved just leveling up my character and killing monsters, collecting the best items possible and so forth. I, sadly, never managed to complete the game, as it started to get pretty hard. I would play it now, but I don't have the urge to anymore due to how dated it looks...
3. I've had some heated battles against the AI in StartCraft. I remember playing hours alone just Skirmishing. I never played the campaign - too hard!
4. In more recent years, I bought my PS2, and GT3. This is when my racing and overall car passion started. If that guy in the game store never recommended GT3, I may not be here right now. I was a pretty poor player at first, but quickly gained in ability and had many, many long hours on that game. I think I got to 80%+, but never finished it.
5. I used to play Unreal Tournament 2003/4 quite a bit. I finished the championship several times, but never got bored of it. About 2 years ago, I started playing online. Everyone was too good for me... it was unbelievable. I would be playing right this moment, but this darn PC and its overheating and reliability issues is a point of its own.
6. Final Fantasy games, in particular 8 and 9, I had some great times with. In FF8, I perfected - all characters were level 100, and the end boss was beaten easily. The only boss I think I never beat was Omega Weapon, but that was so bloody hard and relied on luck that I gave up pretty quickly. In 9, however, I beat the hardest boss in the game (it looked like a multi-coloured bouncy ball. I cannot remember the name). That required some luck too, but after 10 hours straight I beat it. At one stage, when I thought I was doing well in one of my attempts, my brother's friend walked by and tripped over my controller's wire, un-pugging it! I was very annoyed!
7.Next is Final Fantasy 10. Leveling up to get all the equipment, and to defeat all the Dark Aeons was very time consuming, but I loved it. There must be 200+ hours on my save game alone, but I still didn't get even half way to where I wanted to go. I take my hat off to people who have the dedication to go all the way...
8. Most recently Gears of War has taken me over. This is the first game that I have properly played online for long periods. You get your frequent spells of idiots, but it's awesome fun when you're on a team with great guys. One in particular was when everyone unfortunately left, so it was me against one other guy, on a difficult map: Canals. It was pretty great - I wish they allow 1 vs 1 as an actual option, because I've never had so much fun since!
9. Most recent, must be the UKGTP Lan meeting. This must be the only experience I've had with gaming outside the household, so it was made even more special. Everyone was competitive and sensible while racing, while being friendly and silly (

) outside of it. I would most certainly go again if possible!
10. For the future, no doubt Forza 2 will keep me gaming for many hours indeed. I am dedicated right this moment to complete the game and to race you guys online. If only my broken Xbox would arrive sooner...