The OLDER KLRs had oil usage problems, but it wan't consumption, it was blowing oil out of the crankcase breather into the filter box, then leaking on the ground. It wasn't burning it.
I ride a converted Kawasaki KLX 650, it was a dirtbike with head/tail light, then I made it legal to ride on the street. My father-in-law runs a Honda XR400, and had a XR 600, both street legal.
They are a blast to ride on the street. Light and quick. I get about 44mpg avg with a 15/43 sproket combo (14/50 stock).
Some bombproof bikes are the Suzuki DRZ400 and Honda XR400. Little maintainence is required and the valves do not require shims to be adjusted. Both have a large aftermarket. The DRZ400SM is very popular, ready to hit the street. The old XR400 are also very popular, but were never available street ready. Suzuki also makes the DR 650 as well as Honda's XR 650L can both be had street ready. Honda also makes a 230L that is street ready, just a smaller motor.
Kawasaki has the KLR 250 and 650 (more street than trail). BMW has the GS 650 (expensive but better ride). Yamaha TTR bikes are small bore dual-sports.
The Yamaha WR bike is a rocket, a blast to ride, it makes good power, but will not have as good economy and costs more to maintain than the others, just a more powerful semi-race motor. People have even been legalizing the Honda CRF and Yamaha YZF motocross bikes. Yeah they rip, but constantly maintaining the bikes suck. Don't forget Aprilla, but expect to turn the wrench as much as you turn the throttle (almost strictly a supermoto race bike).
My recommendations (not necessairly in this order):
Suzuki DRZ 400 and DRZ 400 SM, DR650
Honda XR 400, 230L, 600/650, and 650L
Kawasaki KLR 250/650
KTM 450, 560, 690 (can come from factory road ready)
ride a barely legal KLX 650