If you want to run an SLI configuration, you can only use graphics cards with the same GPU model. Different graphics card manufacturers aren't a problem, but in a worst-case scenario, the hardware revisions or graphics card BIOSes may not match. The clock rates may be an important factor, as well. The first card (the one closest to the CPU) is usually the "master" in the configuration. If this card is overclocked, there's a risk that the second card will try to reach these speeds, too. If you suffer from frequent crashes or overheating, you should try adjusting the clock rates of the master card to match those of the second card (or even slower) and see if this makes the configuration more stable. Moreover, both cards have to have the same frame buffer, too.
AMD cards can be mixed, but you have to stay within the same series, as indicated in this chart. We tried pairing a Radeon HD 5800 card with a 5700 board, and of course it didn't work. Pairing a Radeon HD 5870 with an HD 5850 or an HD 5830 works fine, though. Whether this makes sense is debatable, given that a CrossFire configuration is at best only twice as fast as its weakest card. At least the flexibility is there, though. You can buy a cheap Radeon HD 5830 today, and, once prices fall, upgrade the computer with a Radeon HD 5850 or HD 5870.
The different combinations worked splendidly in our tests. With AMD graphics cards, you usually use the fastest one as the master card. The performance increase by doing this is very small, but it can be seen in all the benchmarks. Again, running a differently-clocked CrossFire combination might cause some issues due to higher clock rates of the master card. You need to either change clock rates or change the card sequence to fix this. We needed to do this with our three-way combination of the Radeon HD 5830, HD 5850, and HD 5870. The Radeon HD 5870 was rejected as the master card. Only when we used it as the third card in the configuration did it work properly. This arrangement doesn't really have an impact on performance, since all three cards will slow down to the speed of the Radeon HD 5830.