To start, check with your auto and/or home owner's (renter's) insurer.
I think that most people don't have specific cycling related insurance ... i.e., theft is usually covered by the homeowner's policy -- the deductible may be larger than the replacement cost, so a 'rider' to the policy may be needed if you want a bike/whatever to be covered. A good lock helps when you leave the bike in a public location!
Injury is hopefully covered by your existing medical OR the coverage of the driver (!) who hits you.