I was going to make this a poll and thought better of it. I figure that I would miss someones favorite so I nixed that thought.
I'll start out.
Obviously I like the Shimano 105 Group for Road bikes. Strong, durable, and at a fair price. I LOVE the higher end stuff, but stick around a year or two and you'll have it in the 105 Group.
For MTB and such, I am split. To be sure, the Shimano LX group gives almost the same as the 105 group in the value arena. But, I really like some of the stuff I am seeing in the SRAM "X" series, so much so that my MTB frame will have a X.7 long cage rear derailluer and Shifters put on it.