I specifically like to pay for my car insurance monthly, so I'm an ideal candidate to answer this question. I have the independent means to pay for the policy on an annual basis, but prefer to use a monthly direct debit.
Paying monthly appeals to me as it gives me a degree of flexibility. Firstly, my car is quite old and I have a nagging suspicion it could give up on me at any time. This means I will have to buy another one and therefore alter my insurance. If I have already given my insurer a large amount of money for an annual policy, I would then be in the position of having to stay with them, or even arguing with them to get money back. I don't like to be in this position. By paying monthly if I have to move insurers for any reason I can do so. They may try to charge me a cancellation fee, which I accept, but my logic is that either way I'm in control.
The premium I pay for insuring this way is around 28% APR. Although this is a hefty premium when I could pay annually, I still prefer it. It gives me a clear payment per month, rather then a hefty unexpected bill each year - and I prefer the convenience it gives me as opposed to the overall cost.
With my car being relatively low in value, I have always chosen the cheapest insurer I could find on the market. I was initially named as a driver on a family member's policy to keep costs low, before finally taking my own policy in my mid twenties. The cost for newly qualified drivers is so astronomical that I personally wouldn't pay it at all - I would use public transport over paying £200+ per month as a teenage driver.
The insurers I've used recently are Elephant and 1st Central. I found both of these through price comparison sites such as compare the market and confused.com. Elephant offered a seemless experience over the phone, taking me through the eligibility questions before setting up my policy. However as I recall they increased the price year on year quite drastically, until I decided to shop around again.
Most people I speak to would much prefer to stay with their own insurer rather than have to shop around, but only do so when their premiums become prohibitively expensive. In my case when I shopped around again on price comparison sites I found 1st Central as the cheapest and now only pay around £23 per month. Their customer service seems quite a bit 'leaner' than Elephant in that they do a lot by email with not a lot of after care, which is fine by me because I'm only really interested in the lowest price.
In my policy I'm not at all interested in add ons or extra cover. I know there is some sort of window damage cover in my policy, however when I was recently broken in to I decided to find a cheap local garage instead. This was cheaper than paying the excess and potentially losing my future no claims bonus.
I wouldn't actually take a car insurance policy at all if it wasn't a legal requirement. I understand it's essential to cover in case of third party damage, but in the case of my own car I prefer to keep this as cheap as possible. This means making my own repairs, running a low cost and low maintenance vehicle. In fact I have actually looked in to the possibility of a motorcycle - however safety concerns mean I need to use a car.
I am still with 1st Central and now in to my 3rd year I believe. I will continue to use them as long as they keep the premiums relatively low. If I had an expensive BMW I would consider a more robust insurer, where I know I can ring up and get super-fast service. However for someone like me who likes to run a low cost car and doesn't intend to make any claims unless it's a disaster, they're the ideal insurer. I don't bother them and they don't bother me!
Without price comparison's I would probably have just gone to the local bank or broker and been paying a lot more, so for people with my goals for insurance price comparison websites are a wonderful tool.