There are some independent pet insurance companies out there, just Google it. I get pet insurance through my company. There is a deductible and it covers major procedures, like if JoJo broke his leg and needed x-rays, surgery and pain management.
Some Vet offices offer Puppy Insurance that covers the puppy until age 1 year. It's like $15/month and covers all the routine visits, vaccinations, and sometimes the neuter/spay.
Hope this helps.