*This links to Jim Zondag's amazing white paper, "2015 FRC Championship History", I will use it as a proof for my picks, but everyone that cares about FRC history should look it over.
http://www.chiefdelphi.com/media/papers/3133?
1. 67- the HOT team is #1 by a clear margin. They have been the definition of greatness their entire existence. Their rookie year they won all stars at champs. They then won 9 regionals, 15 districts(TBA has some missing since they have 27 combined wins, 2nd most behind 254), 4 MSC's and 3 MSC finalists (thats 7/8 finals at MSC). These stats are more amazing considering crazy high the level of play in FIM and the pre-FIM regionals at Detroit, Midwest and Great Lakes regionals. HOT also has the best overall championship performance of any team ever, even better than team Hammond. Yes, you could make the argument for 71 if you value championships more heavily. (This next part is all in the whitepaper.) However, if you look at the theoretical district points a team makes playing in eliminations, then it shifts to HOT. HOT has had the point lead since 2008. At end of 2015 champs HOT had 577 compared to #2 Poofs at 516. The "time derated points" table is even more convincing. Since 2005 HOT never is worse than 5th best. They have the top score ever at 161 at the end of 2010. They also had the highest "time derated points" for 6 separate seasons. If you don't like statistics and like "the eye test" HOT may be top in that too. This is purely opinion but HOT did do many amazing things like: won 2010 champs in the last seconds by beating the basically unfair 1114-469 combo, made the bridge auto a thing first in 2012, fed themselves balls all of 2009, combined arguably the best FCS and a 50pt climber in 2013, the pitchfork 2005, caping 1241 at Palmetto 2004, ect... And don't forget they're in the Hall of Fame.
2. 71- 4 world champs, dominance at champs and regionals. The Beast.
3. 111- 3 world champs, Hall of Fame, dominance at champs and regionals. Their 2011 robot was the most inspiring one I have ever seen in real life.
4. 254- 2 world champs, 15 SVR's, 16 other regionals, Hall of Fame. Where does a team even hang 41 blue banners.
5. 1114- 1 world championship, Hall of Fame, 26 regionals, 39 blue banners. It's Simbotics.
Throughout the history of FIRST, if you took a poll of everyone participating in FRC asking, "Who is the single most iconic team?", almost every year it would be between 67, 71, 111, 254 or 1114.
Honorable mentions: 469, 148, 118, 233, 987, 33, 217, 25, 16, 27, 177, 365, 341, 51, 359, 2056