It really depends on your level of tolerance, and your situation. People without the ability to self-insure probably need some level of insurance, depending on their situation. With a stash, you have the ability to self-insure. It is also worth looking into what you are automatically insured for. For instance, many years ago the express bus from Melbourne to Sydney smashed into the back of my car while I was waiting at a green light for an ambulance that was already halfway across the intersection. I had whiplash for 3 years, which reduced the amount I could work to about half time. TAC would usually have paid the difference between my earnings over those 3 years and my salary (it didn't because of my personal circumstances). Income protection probably wouldn't have paid anything.
Life Insurance - why with no dependents? But with dependents there is a case, and superannuation is cheaper because it is pre-tax.
Income Protection - if you have a stash, you might not want it. A work mate was out bicycling on a dirt path with his son, fell down an embankment and broke his neck - he didn't have much put away, and income protection saved his lifestyle.
I'm slack with house and contents insurance, vehicle insurance and NRMA membership, in that I almost certainly could/should get less (with more excess), and shop around for a better deal - but I haven't. I think I've had claims against each policy at some stage (not sure about the vehicle policy). Last year I got back a lifetime's worth of NRMA membership payments when I had a problem in outback NSW.