Kenmore's seem to be the most common vacuum we see in for repair.  Lots of hose issues with the canisters, especially burnt contacts and wand cords and/or broken handle tubes.  A close second would be brushroll issues with the Kenmore uprights and canisters thanks to melted plastic endcaps.

We also see a lot of bagless plasti-vac's (Bissell, DD, Hoover, etc...), but other than belts, we'll generally refuse to work on them. 

Here in Canada, there is no service for Dyson, Shark and LG.  These three companies handle all of their repairs themselves, requiring vacuums to be mailed away when something has gone wrong.