The question needs clarification from multiple angles.
First, let us know that insurance as it is used in today's context is something that never existed during the time of our noble prophet (s) and the best generations after it. So you'll not be able to find a direct context that relates to the qur'aan or hadeeth.
Next, we see what insurance is... In the modern context, insurance is where you pay a regular fee (usually monthly) known as a premium. Then if something goes wrong, like an accident, you are compensated with an amount which may be BIGGER or SMALLER than what you have paid as premium.
Well, that's the standard case. But there are a lot more strings to it. For example, if you don't claim, there's the bonus, then there's a discount in the premium, then there's an additional insurance and so on... These extras vary from country to country and company to company.
Now, what do the scholars of sunnah say about this? In general, all scholars of the sunnah have warned against insurance. What are the reasons for saying no to insurance? Here are some...
- First, scholars state that this is like a gamble. You are challenging the insurance company that you're going to make money out of the deal and they do the same.
- There is deceipt. People making false claims and a lot of cooked up stories.
- There is gharar and uncertainty.
- Riba. You claim more than what you pay.
So insurance in general is considered haraam. But now comes the situation of third-party vehicle insurance. In many countries, one is compelled to make this payment whether or not you are going to make a claim. So it is more like a requirement in order to use your car on the streets. Without it you cannot drive.
Thus comes the deciding factor. Do you need to drive a car or can you do without it? This is something between you and Allaah. Another person can't answer that question for you. IF you are forced to drive a car for basic needs and you cannot do without insurance as compulsion, scholars say that there's no harm in it. But you cannot go for full-insurance and you cannot make any claims.
This is s very broad subject and you can find a lot of cases here: http://www.islam-qa.com/en/cat/316
And Allaah knows best.