Hi, here's my two cents, and I'm in the insurance and financial planning business: disability insurance is always a good idea - both short- and long-term. Here's an analogy that always worked for me: I assume you have auto insurance and homeowners insurance if you own a home? Well, what's more important to insure? The "goose" or the "golden eggs"? You can alway buy more possessions if you can earn money. If you can't earn money, that's a real problem. So make sure you insure your ability to earn an income before anything else! Even life insurance! And get it as soon as you can before you develop health conditions that would make it difficult and/or cost prohibitive to obtain (you'd be surprised how many people can't get it or have to have exclusions on their policies).
As for other policies, for such specific situations as accidents and cancer, I would only sign up for them if you are VERY risk averse and you have ALL your other financial needs taken care of (emergency fund, adequate retirement, disability insurance, life insurance etc.) Why do you need "extra" money just because it's cancer or an accident as opposed to some other equally devastating disease?
Just my humble opinion - hope it at least gives you food for thought!