Insurance might feel like money down the drain, but having been caught out without it in the past, let me tell ya: I learned my lesson early on. It's one thing my family wasn't really big on, and so it's been a case of self-education in my 20s.
Contents insurance (for your crap)
So important IMO, and increasingly cheap. I'm seeing affordable renters' policies advertised in mainstream media now, which is a new trend, and a good one.
Our flat was burgled while I was at uni and I lost a few things, most devastatingly, my laptop. Annoyingly, I had been pondering taking out contents insurance but decided we couldn't really afford it at that point while scraping by on a student income.
I took out a contents insurance policy after that incident and it's served me well since, through multiple break-ins and claims over the years. The cost dropped to just a few hundred dollars once I bought my house, which was a nice surprise.
Plus, if you're still flatting, contents insurance can cover you in the event that you cause damage to the property you're renting (just in case you inadvertently cause a fire, flood, that kind of thing).
House insurance (for the most expensive thing you'll probably ever own)
After working my ass off to be able to have a place to call home, you can bet I want to protect it in case of fire, flood, earthquake or whatever else might jeopardise the roof over my head. (Also, the bank doesn't give me a choice :P)
Life insurance (for what you leave behind)
To cover my mortgage in case I cark it. I don't have dependents but this obviously becomes infinitely more important if there are kids in the picture.
Trauma/disability/income insurance (for your moneyyyyy)
More expensive than life insurance, but arguably more important. Financially speaking, your ability to earn is probably your biggest asset ... and yet we often don't take the appropriate steps to protect this.
ACC is meant to cover you if you have an accident but I can't say I have a lot of faith in them. As we learned, it needs to have a defined cause - we lost out on a full month of income a few years ago when ACC refused to stump up a few years back. And it doesn't cover illness, which is obviously another huge threat to your income - they say that illness stops far more people from working than accidents do. Plus, if you're made redundant, you may not be able to get unemployment benefits (if you have a working partner, as again, we know all too well, and there are probably other exclusions too).
Insurance can help replace your income in the event of temporary or permanent disability, or illness. It's not something we generally talk about, but I bet you more people than you think around you have income protection insurance (and a lot of those who don't, quite possibly should). Redundancy cover, from what I've seen, is less common and quite pricey, but there are also rent/mortgage protection policies that can help cover your biggest cost, at least.
I prefer to pay my insurance premiums annually, and they almost all fall sometime in the first quarter of the year.
It's a painful hit to absorb, but when I ask myself how I would feel if I wasn't covered for at least the very basics, my gut instantly reminds me that I'm doing the right thing for peace of mind.