I just recently purchased pet insurance through Embrace for my whippet, Devo. I ended up getting it because he had recently been nipped by another dog while playing and had to get $400 dollars worth of stitches. While I have not had to use the insurance for any accident or illness claims I did take advantage of the wellness program, it's sort of like a "dog FSA".
The claim process for his wellness reimbursement was very easy and quick. I had the check in about 2 weeks from the time I submitted the claim.
I also had Devo go through a medical review, Embrace reviewed his past year's worth of records and provided me a detailed outline of what pre-exsisting conditions would be covered and when. This way if something happens but it was a condition he had been seen for before I won't be surprised if something isn't covered.