Dream Theater: 53 times
Queensryche: 19 times (last time was in 2009)
Rush: 18 times
side note: in addition to the 47 times I saw MP with DT, I also saw him perform at 20 other shows in LTE, G3 (with JP), Transatlantic, Neal Morse, Adrenaline Mob, Cygnus and the Sea Monsters, Amazing Journey, Yellow Matter Custard, PSMS, Flying Colors and The Winery Dogs.
As for the greatest distance I've traveled, in the past it would've been from SoCal to the New England states (and then road tripping to several shows while there) but now I'd say internationally (3600+ miles one way).