I had a really bad ticket three years ago and lost my insurance. I've been with Progressive since then, and am pretty happy with their rates. Not the best, but it could've been MUCH worse. Of course, I have a clean record with the exception of the one ticket. I don't know what you should do if you've got several violations.
however, even though it's been 3 years, when I've gone insurance shopping again, I'm finding the rates are outrageous. Some companies use different timelines for "risk" factors. I probably won't be in the clear for another couple of years.
good luck