We've had GEICO for about 8-10 years. I have filed two claims with them, and they were pretty good. The repair shop we would have used anyway was one of their designated repair sites, so we just took it to them for an estimate, GEICO approved it, it was scheduled and paid for (minus our deductible). Our rates, which had dropped just about every year, have gone up some since the claims (within a year of each other). But that's reasonable, since our pattern of service has changed.
You can manage your account on-line, and they waive the monthly payment fee if you set up electronic billing and payment. That works well for us. One little gripe I had was when we had paper billing, the statements would often come about 10 days before the bill was due. I typically pay all my bills on payday (every 2 weeks), so occasionally I would get a bill just after I had gotten paid, and I had to make a special payment so I wasn't late. Every other bill I got usually came about 20 days before the due date.