I don't have pet insurance, but it has crossed my mind as something to get since I have a dachshund and there's always going to be the possibility of a back injury.
However I don't really like insurance companies and I'm a bit reluctant to give them my money unless I know they will pay out. For instance with my car, a week after I bought it, someone in a car park reversed into me and the insurance company claimed equal fault so they wouldn't pay out (based only on what gear my car was in). Someone also keyed my car, on the extreme opposite side of the city where I never normally go, I had no idea who keyed it and it was in a massive parking lot so it would've just been some random being a jerk, but the insurance company then said I was too risky because it might happen again (I couldn't take out a new policy with anyone else)! So I told them to stick it, and I no longer have car insurance and instead I pay myself insurance for my car, at least I know there's money there if I need it and I won't have to jump through any hoops to get it! it's more of a piece of mind for me to save my own money and know that it's there for whatever I might need it for, yes it sucks if you have to pay up for something unexpected and costly, but I'd rather rely on myself than companies who try and get out of it by any means they can. Mind you I'm religious about where my money goes and I always have a stash of 'just in case' money to cover most minor things.