As other people have said it really depends on what you bring over.
If you are a repatriating Cypriot and have owned the vehicle for 6 months before you come (you will also need to show this not only from the log book but proof of purchase and an old insurance certificate too) you can bring the car in duty free but you will pay for registration and plates. The prob is that if the car has a larger engine and is relatively new then these costs can be pretty steep.
If you don't qualify under the 6 month rule then you can bring it as a repatriating Cypriot with an allowance taken off the duty payable. By why of example we fetched our Mercedes C200 (2007) model adopting this method and received an allowance of 5125 euros from the duty payable which effectively meant there was no duty payable barring the 0.036 cents per cc which is charged on every car.
It was a lengthy process and you do have to pay an agent to do the paperwork as Customs will not assist regardless of how you bring the car in. The process agents are located next to the customs in Nicosia so not too hard to find but it is a long waiting exercise - cost around 70 euros for them to submit relevant declaration etc. You also have to get an emmissions certificate as this gives you an extra 20% off when submitting the car through customs again regardless of how you bring the car in ( this is obtained from Ministry of Transport) so you make an application at Customs go to MoT for emmissions certificate before going back to Customs to get the application through. Once through the customs stage you then have to get an MOT at any garage that does them. The MoT tests here are basically assessing brakes and emmissions so not so stringent and the certificate issued is valid for 2 years in Cyprus and costs 35 euros (provided nothing extra needed for the car to pass).
Once this hurdles are negotiated you register the car back at the Ministry of Transport and this is where you pay for the registration, plates and road tax. Our vehicle was an 1800cc engine (UK registration 2007 and manufactured 2005) and worked out to be around 550 euros including 6 months road tax. I also brought over my Volvo S40 (2001) and the age and smaller engine worked out well in my favour as the duty payable was 220 euros and whilst I have MOT, I've not managed to get to Ministry of Transport to get this registered as they only work till 1pm and it's a bit hard to get time off work at present but I expect the registration for plates for this older car to be a lot less than what I paid for the Mercedes although road tax will be around 48 euros for six months.
If you are going for sporty number or a larger car the rates are a lot higher and the road tax is also a lot higher but unfortunately I cannot tell you these rates.
If you are not a repatriating Cypriot I think you can bring the car in duty free if you are retiring but again be ware the registration, number plates costs are relevant to the actual size of engine and car. I did hear of a retiree bringing in a Range Rover Sport (quite new) duty fee as a retiree but was charged a massive 8000 euros for the plates and over 1000 for the road tax - ouch! - don't forget that will be a yearly cost too.
There have been mummerings that the Government is looking to abolish import duties for those people bringing in cars for their own use but nothing has been disclosed so doubtful this will happen any time soon and I bet the registration process will still be costly on newer larger engine vehicles.
Also note for you is that pick-up trucks are treated far more favourably tax wise as they are deemed to be for agricultural or commercial purposes and as such receive much lower bands of import duty. Again beware the engines are larger, so registration of plates could be costly - I don't really know too much about this just what I was once told by a guy who brings these vehicles in as a side-line.
One last thing I would say is worthwhile is to check out the Ministry of Finance webiste as they have on-line calculator to give you an idea of the duty payable on any given vehicle you decide to bring in. It is in english too and if you do get stuck simply call the Customs office and they should be able to give you an idea of the cost of the duties to import at least but doubtful they'll be able to tell you registration costs.
Hope this helps