One of the most advanced disk rotors are "floating rotors", made of 2 different materials and connected together. Look like this:
These are exceptional brakes rotors. They are very rigid, won't bend sideways easily. Overheating is much less of a problem for these boys. But if they are getting overheated, they don't bend that much because of the material expansion. Usually the spider in the middle is made of aluminium alloy, but you can get rotors with carbon core. Carbon ones weight less, but cost a lot more than with alloy spider.
Also you can get a full carbon rotor:
These are very expensive. Marketing materials for these say they are perfect, but you can easily spend a lot of money only on one rotor. I have never tried a carbon rotor or even seen one in flesh, only on pictures. You can also get a combination of carbon with ceramic spider and other space-tech materials. kettlecycles.com provide with examples of these. (Thanks @J-unior for the link)
One of the extremes I've seen is combination of carbon and ceramic in a disk brake rotor. Don't really think these are available in shops, but interesting to know.
If you go for single piece cheaper rotor, then you don't have such a big variation in materials: they are generally made of stainless steel. And here the shape is making a big difference.
If you get one of these:
You'd be able to stop on a dime, but you don't get a lot of modulation. These things will be like on/off switch if combined with good pads. These are Hope trials rotors and I would not recommend using them for anything other than trials. (If you are doing trails, you should already know this)
Then you have middle ground rotors with a lot of variations on patters:
These are the most common and most affordable with prices from £12 to £25. I do believe that in this category there is really not much difference in quality. But make sure that the pattern has overlapping holes: when the disk is dragged through the pads, there should not be a continuous line of solid material. Pads should have a way to clean themselves and if in a section of a rotor there is no gaps, pads will not self-clean, decreasing the overall performance. In this category choose the ones you like most.
And the last in the category are cheap and nasty rotors you get on bikes from WallMart or Asda. They are usually heavy, easy to bend, with poor pattern. Look like this:
Apart from the material and type of construction don't forget that you have different diameters of the rotors: 145mm, 160mm, 180mm, 203mm and 205mm. The bigger the rotor, the more braking power you get and better heat distribution, but also the greater the weight. Usually downhillers go for 205mm rotors on the front and 180 on the rear. For more calm disciplines like XC 160mm rotors are more common.
The size of the rotor must match your current one, but you can buy an adapter to place you disk brake caliper in the right position for the size of the rotor.
And you can get different types of mounts to the hub. The most popular is 6 hole international standard - on all of the rotors above. But you also get Shimano Centre Lock:
For this type of mount you need to have a hub with the same mount or use adapters from 6-bolt to Centre lock. About 8-10 years ago there used to be rotors with 5 and 4 holes for mounting, but you won't get them now.