I've tried this post a couple of times; let's see if this one pans out.
If you look at 2000-2004, the answer is simple: 71. When you win three of the five Championships in that timespan, two of them with robots who seem to take perpetual residence on best-robots-of-all-time lists, it's not a hard question.
In the second half of the decade, it's not as easy. While 71 has by no means rolled over and died, they haven't met with that same level of success at the Championship. Instead, we see the rise of 217 making appearances nearly every year on Einstein (2007 being the exception), along with several other teams making their presences felt on the regional level.
But if we're talking about the decade as a whole, and with all my biases known, I think the winner has to be 67. Let's lay out the
high points--ignoring all the other hardware--of their seasons this decade:
2001: UTC Finalist
2002: Championship WFA (and getting beat by Beatty in division eliminations--hey, stuff happens).
2003: Division Finalist
2004: Division Champion
2005: Championship Winner
and Championship Chairman's Award (beat that!)
2006:
Just winning the
Great Lakes Regional.
2007: Division Finalist
2008: Championship Finalist
2009: Championship Winner
Going back to when 1114 was just shining up their Rookie All-Star trophy, 67 has been among the top eight alliances on the championship level all but one year (a year that threw a lot of great teams for a loop), while being one of the few teams to have won the highest three awards in FRC between winning the Championship, Chairman's, and WFA*. I don't think anyone can bring up a team that has been that successful that consistently over this decade.
*111 did it a year later when Dan Green won WFA, and the newly-formed 51 can claim it as well with their combined history. (47 won Chairman's in 1997, 65's Ken Patton won WFA in 1999, and 65 won the Championship in 2003.)