There seems to be many misconceptions accumulated in this thread.
First, the biggest burst depth killer is the High ISO noise reduction setting. In older cameras, setting it ON reduces the burst length significantly. In newer cameras, the settings off, low and standard are OK, but setting it to high again kills burst rate. This can be seen already on the burst depth prediction display the camera has.
Second, the speed of the memory card doesn't affect burst depth very much, especially not when shooting RAW. Most Canon EOS cameras don't write to the card and shoot RAW simultaneously. But the speed of the card has a significant impact on how long time it takes the camera to recover from a burst, and be ready for the next one.
When shooting jpeg only, card writing and shooting is usually done concurrently, thus a fast and well working card improves the burst length to some extent (see the burst length data below).
Third, burst depth is never harmed by using a long exposure time. On the contrary, if you are shooting jpegs, it gives the camera time to write to the card while the action has stopped waiting for the exposure to end. But frame rate (images per second) is of course very sensitive to the shutter speed. You usually need at least as short as 1/500 s for the camera to run without the frame rate being impaired by the time it takes to expose the sensor.
Fourth, all other settings will not impair burst length. But using Servo AF on tricky subjects will impair frame rate, since there will be a little longer delay between each shot, whilst the camera is fighting to figure out how to focus. Somewhere above it was said that simpler cameras don't have any focus priority setting, but that's also wrong. Focus priority is the only setting they have (now I'm talking about the focus priority setting which was available until the introduction of the 1DX - that camera is different). What these cameras lack is the release priority. Thus they always allow the camera to make a few repeated attempts to figure out focus, prior to taking the picture.
Fifth, one of the primary differences between the higher rank cameras and a model like the 700D is the buffer memory size. Cheaper cameras simply don't have the memory to keep running like the more expensive ones.
Here's the burst data for the 700D:
Based on 8GB memory Card:
JPEG Large/Fine: Approx. 22 Shots
RAW: Approx. 6 Shots
RAW+JPEG Large/Fine: 3 Shots
Based on 8GB UHS-I memory card:
JPEG Large/Fine: Approx. 30 Shots
RAW: Approx. 6 Shots
RAW + JPEG Large/Fine: 3 Shots
You can also see that having a faster card improves the situation when shooting jpegs, but only for jpegs.
Now let's look at the same specification for the 7D (which fires eight frames per second, thus produces quite a bit more data each second):
JPEG (Large/Fine): approx. 110*/approx. 130**
RAW: approx. 23*/approx. 25**
RAW+JPEG (Large/Fine): approx. 17*/approx. 17**
The figures marked with ** are for a faster card (UDMA 7). Not even dual Digic 4 processors make much of a difference between different card performance when using RAW, but it's obvious that the capacity for shooting long series here is much higher.