The whole time that I was learning to wield a camera and capture sound in college, I was always told to record sound separately when you shoot with a DSLR. Every bit of research that I did outside of school (generally reading books or watching videos by sound engineers) reinforced this mantra. As a standard practice, I would still recommend having a separate system/device, and possibly even a person, to record sound. However, the reality for most of us is that we are usually a one man show. Let me quickly explain the difference between options. .
Sound can be either recorded single-system or dual-system, generally. Single-system sound means running the microphone directly into the camera, which can be done with higher end cameras with no problem, usually via a XLR input on the camera.
DSLR's really aren't built with the processing power for sound that other cameras which are strictly built for video have, and they don't have the balanced inputs. So, generally speaking, you don't want to record sound in-camera with a DSLR. However, there are people who do it; albeit, I was never one of them - until now.
At my station they use something called a BeachTek Box. It's a small box that acts as a preamp for an audio signal running into your camera. It looks like this:
You run mics directly into the XLR input on side, the box boosts the signal (and limits it in some cases), and then sends it into the camera. I've heard that lower-end versions of these can be pretty noisy, but I have to say the BeachTek box works amazingly well. I've used it with shotgun mics and with wireless lavs and the sound is amazingly clear. I was pleasantly surprised. Even to the point where I can't decide if I want to purchase one myself, or go with something like the Tascam DR-60D or the Tascam DR-70D. To me, the biggest issue would be price. The BeachTek DXA-SLR Ultra runs right about $300, and the Tascam DR-70D can be found now for about fifty dollars lower and has four inputs as compared to two. The DR-60D only has two inputs like the BeachTek, but is half the cost.
B & H photo gives a great demo of the BeachTek DXA-SLR Ultra here;