Had them for over 20 years, very satisfied and they handled the few claims I've had quickly and easily. This is when someone hit me, or for a car breakdown, so I don't know how they handle accidents where their insured are at fault.
Customer service is stellar from my experience. Call at 6am on a Sunday morning, get a live English speaking person. Call at 2am on a Thursday, same thing.
I price shop every year or two and can't beat them. Nearest competitor when I looked last year was over $200 more for less coverage. I have two vehicles, just recently renewed the policy (older vehicles, collision coverage on both, with auto club for roadside assistance which is towing/lockout/breakdown on both and higher than required liability coverages) and pay ~$23/per vehicle per month total. I also insure my house through them (my area's home insurance partner for them is Travelers) and they are AWESOME. But I know that makes a difference if you're carrying a multi car and home insurance as bundling gets you cheaper rates, and my longevity with them also knocks down the pricing.
I push for my discounts tho. I call them up and we fine tooth the policy and that's after I go online and play with the coverages through their site. They let you add/remove and see how things cost out and you can save quotes without applying them - they're stored in your user ID. I got one rep that actually found a regional coverage through GEICO County Mutual (it's still GEICO, but they have regions that differ? Yeah, I don't get it either) but it literally cut my 6 month premium in half, and the only loss to the coverage was accident forgiveness. Um, yeah, I'll take it!
I have been hearing about a new company called Root, that only insures good drivers and require you to allow them to monitor your driving for a few weeks before they'll even offer you a quote... or outright refuse to give you one if your driving is deemed undesirable. Sort of intriguing as they claim to get you more than 50% off standard insurance policies because they won't insure anyone that drives poorly/has a record of past accidents. I may be looking into them at some point because we also drive very rarely at this point and the one thing I know for sure is as of this year, GEICO doesn't care about minimum driving; it is either you drive the car for work or for recreation (two categories as I've understood it). I've told them I drive less than 2K a year and they don't go off of actual (low) mileage; they just put in that vehicle is "occasional/vacation use" which could mean you drive it only on the weekends but could still rack up 10K a year...