Limitations on Clip Length
Many cameras have limitations on how long you can record video, as a precautionary measure to ensure that the sensor doesn't overheat. Some cameras have a video-file cap of 5 minutes, some run for 10 minutes, and some cameras have no clip-length restrictions. This can be annoying and frustrating, but on the whole it's not that bad; as long as you're aware of how long you have left to run, you'll be okay.
I came from XDCAMs, on which you have at least 45 minutes of HD-quality video to work with every time you press the record button. Reducing the clip length to 12 minutes or less was a bit of a shock for me at first. But then I remembered shooting on film, where you'd often have only a 5-minute or 10-minute reel to shoot on. I just fell back into that filmlike mindset of not recording long takes, and cueing up action just as I was about to record. It's a bit stressful at times, but it can also be good fun.
Choosing the Right Storage Media
The main video formats used in DSLR video capture are H.264 (a QuickTime wrapper for MPEG-2 video), AVI, and AVCHD (stored as .MTS files). All of these formats have their issues, and none of them are perfect. The main thing to consider is how you plan to edit your footage.
Some nonlinear video editing (NLE) systems (that is, systems that can perform random access on the source material) will accept any of these formats, but most footage has to be converted in some way. This process consumes both time and hard-disk space. I use third-party software to convert my clips into a file-friendly version before I start to edit, which not only makes the editing process quicker but also frees up my edit machine so that I can carry on with other edits.
As for the actual cards used in a camera, some DSLRs use CompactFlash, while others use SD/SDHC. In all cases you need to consider the card very carefully: The card is the equivalent of tape stock, and the more you spend, the better your chances of not losing any of your video.
As a rule of thumb, most video is captured at a data rate of around 24 megabits per second to 40 mbps. Cards that can cope with that speed are pretty expensive, and cards that have enough storage capacity to hold all of your video are also pricey. For the speed side of the equation, you'll need at least a Class 6 card if your capturing bitrate is greater than 32 mbps; you can get away with using a Class 4 card if your bitrate is less than that. As long as the write speed on the card is higher than 40 mbps (that's Class 6 and higher), you should be okay using it with any DSLR available today.
I use two 16GB cards, and they're the fastest on the market. They cost around $250 per card; they're robust and fast, and I have had no issue at all with them. On long shoots, I have my laptop and an external hard drive with me, and I dump the footage onto the drive every time a card fills up.
The reason I don't just buy higher-capacity cards is that some of my colleagues have lost data, had cards malfunction, and encountered dropped frames with cards that are 32GB or larger. I wanted to play it safe, because in the worst-case scenario, I will lose only 40 minutes' worth of footage if the card goes down--not ideal, but it's much better than losing the whole day's shoot.