many of the above mentioned overdriven sounds are great. It's all about the song really.
SRV on Little Wing, Riviera Paradise etc too of course.
But basically I like precise/distinct.... but overdriven sound.
To me Robben Ford gets there is a big way: Solo at 3:10, but licks throughout too!
Lots of great examples here. one that instantly comes to mind, and is much lesser known, is the intro to "feels like rain" john hiatt. when i first heard it I thought - that has got to be an old tremoverb or tremolux or something... but having read in an interview with sonny landreth, it's a dumble with a transistor based tremolo in front.