Q1 2000: Vino. One of my early German game acquisition, and a clever and fun business game. Sadly, I haven't played it in over 3 years, though I will have to do something about that.
Q2 2000: Vinci. Acquired this in April and remains one of my favorite overall and certainly about the best there is in the genre of empire expansion games.
Q3 2000: RoboRally. If I had bothered to enumerate the "game of the quarter" for years prior to 2000, it probably would have been RoboRally pretty much every quarter. It still gets pulled out once or twice a year and remains one of my favorites of all time.
Q4 2000: Lord of the Rings. This came out at Essen this fall, the first time I went. I loved the game then, though was a little skeptical about its endurance. I remain about as enthusiastic to play this now as I was then. The expansions have continued to improve it. Sadly, many of those I regularly game with are not as fond of it.
Q1 2001: Battle Line. The first ten times I played this I lost. I kept wanting to play it all the same, and it is by most assessments my favorite 2-player game. (Though the Q4 2005 game may give it a hard run, but we'll see).
Q2 2001: Pounce. I was introduced to this twitch game by a friend and promptly found a copy for myself on eBay. It is best played late at night when everyone is well past a reasonable bedtime.
Q3 2001: Electronic Catchphrase. This got introduced in the groups I play with in July of 2001 and has been played constantly since then.
Q4 2001: Zirkus Flohcati. I picked this up at Essen 2001 and it quickly became one of my favorite fillers.
Q1 2002: Industrial Waste. Another fun business game. Other than the initial burst, this hasn't gotten a ton of play, but I doubt it will be shelved permanently for a long time.
Q2 2002: Puerto Rico. An obvious hit from the beginning.
Q3 2002: Lord of the Rings: The Confrontation. Remains one of the best 2-player games out there.
Q4 2002: Puerto Rico. Everything else remained pale in contrast...
Q1 2003: Fresh Fish. I had played this and loved it in 2002, but it wasn't until 2003 when Plenary reprinted it that i was able to get my own copy.
Q2 2003: Amun Re. This was the big hit of the 2003 Gathering, and while many seemed to burn out on it quickly, I remain fond of it.
Q3 2003: Light Speed. A rather clever speed game, and the best of the "under 5 minutes" set.
Q4 2003: Attika. This was the hit pickup of Essen 2003, whose star has largely faded. I enjoy it more with the 6-free-cards-for-connecting-shrines variant.
Q1 2004: 10 Days in Africa. A great filler and extremely teachable.
Q2 2004: San Juan. Surprisingly outstanding adaptation of the Puerto Rico concept to a card game. Gets as much play as Puerto Rico now.
Q3 2004: Heroscape. The best "toy" game ever.
Q4 2004: Buy Word. There have been a few fairly good new word games in the past few years (Typo, My Word, eg) and this is probably the best of them.
Q1 2005: Crokinole. This has been a big hit since 2001, but the discovery of it by work colleagues and its adoption as a post-lunch game earn it this slot.
Q2 2005: Fiese Freunde Fette Feten. A hugely entertaining and clever game system. All the Q2 plays were on a pre-production copy.
Q3 2005: Fiese Freunde Fette Feten. Finally, it was available, and partially driven by my own enthusiasm, many people wanted to try it.
Q4 2005: Blue Moon. Despite my first two plays of this in 2004 being entirely uninspiring, I retried it and am very glad I did.