Only good things to say about Geico here. When I had an accident, they asked me first if there was a particular shop I wanted my car towed to. I didn't know any, so they recommended one that they have an arrangement with, and an adjuster on-site. Which meant I didn't have to get estimates, or arrange for reimbursement; they took care of all that. They also got me a rental same-day (even though it was Sunday). My only out-of-pocket expense was my deductible, and they recovered that from the other party's insurance and refunded it to me. It took a couple of months for that to happen, though.
Of course, they had no incentive to give me any hassle, since the other driver was clearly at fault (I was rear-ended), and their insurance paid for everything. I don't know whether they'd behave differently if they were on the hook for the claim.
Like jayhawk said, they're easy to get on the phone if you need (and their customer service line is open 24 hours), plus their website is very comprehensive.