Healthy Paws may be newer to the industry, but so far I am very impressed with this company. Their coverage is straight forward and easy to understand - No complicated coverage schedules or limits. Also, they don't have any claim limits for the life of the policy, which is a huge plus and a differentiator to much of the competition.
Claim wise, it would be impossible to be better. I had a large claim within the first month, and once I submitted my puppy's veterinary records the claim process happened fast and furious. My claim was reviewed, settled, and paid within 24 hours. I seriously couldn't believe the level of service.
Healthy Paws also has a cool iPhone app where you can submit claims as soon as you leave the vet. Very cool.
My only suggestion would be it would be nice to have EFT for claim reimbursement directly to your checking or PayPal account. Having to wait for and handle a paper check is a bit dated, and is something to keep in mind if you used a credit card to pay the vet bill (Healthy Paws reimburses you directly after you've made payment arrangements with your chosen vet).
So far, this is an excellent company that I highly recommend. If you are looking at pet insurance, look no further and buy the peace of mind you get with a Healthy Paws policy.