It's not just about the specific make and model of the car, either; what's under the hood may be driving up your insurance rate. Let's go back to my beloved Mini Cooper. If I wanted to buy a new hardtop Cooper, I'd have different trim levels (or option packages) that range from a 121-horsepower to a turbocharged, 208-horsepower engine.
A bigger, more powerful engine means that you're more likely to test it out by driving fast ... and you know the drill. That includes customizing cars to increase their performance, too -- if you buy a souped-up Honda Civic, it'll cost more to insure than a standard version of the same model.
Size does make a difference. A huge SUV won't move as fast as a little sports car, but if you hit someone in it, it's going to do more damage. On the other hand, some people may sneer at mini-vans, but they tend to have lower insurance rates because of the stereotypes surrounding who drives them (I'm talking to you, soccer moms). They also get good safety ratings overall. Actuaries look at crash test ratings, so if your car didn't do too well for its model year, that's going to translate to a higher rate. While newer cars can be more expensive just based on their retail value, an older car may be lacking safety features like side-impact air bags. Yet another tricky dichotomy to consider!
Since insurance companies don't reveal exactly how they calculate rates, what can you do? Your research. Find out if your dream car is also highly desired by thieves and investigate its crash test safety ratings. If you're thinking about buying (or leasing, which can be more expensive because the company leasing it to you dictates the coverage, not you), you can run potential cars by your insurance company to get a quote. That way you won't get a shock after you buy the car!