I've had almost everything... my wife REALLY likes to back into stuff. (to include a police cruiser and BOTH of my Jeeps! bought the JK in DEC and she backed into it in FEB... busted her window, dented her door, NO jeep damage, and she has a nice breeze in her van to this day...) I had good luck with progressive covering a few claims, but then they dropped us...
Geico's claim response was horrific. Allstate got SCREWED by the shop that fixed my wife's truck last time, and I told em, and they did nothing (no bickering about the claim though, as long as it went to the shop they liked... the one that added a bunch of extras to the bill...?)
USAA has not given us any flak at all, we have the lowest deductable we've ever had, because they are cheap enough we can afford it, and they've covered 2 mishaps so far without changing our rate. After having been with them for two years, they also extended the coverage term out to 18 months (I think) at a time, so we hardly ever have to mess with the flippin cards even
If they've opened to non-vets, I'd definitely look into it.