Choosing between a Canon and a Nikon DSLR camera is difficult because both brands have done an excellent job maintaining their status as top competitors in the photography industry. Choosing a brand is an important decision because most of us don't have the financial ability to switch between the two, so once your decision has been made, it's pretty permanent. If you're struggling with this decision, take comfort in knowing that you are getting the best quality equipment in the industry either way.
From what I've found, it really comes down to personal preference. When one brand introduces new technology before the other, the other is never far behind. Before weighing the pros and cons of the brands, make a list of what's important in a camera to you personally, taking into consideration what you'll be using it for, ergonomic preferences, lens requirements, and so on. Then, start looking at individual cameras that match your needs. With each camera model listed, the opposing brand usually has an equivalent model--this is where the details matter.
Keeping in mind that the lesser performing brand in any category may be in such a close second that the end comparison is often irrelevant, there are a few operations each brand currently performs better than the other. For example, Canon has consistently offered better video quality and performs better in low lighting (meaning less noise), but Nikon cameras are known to capture colors more vibrantly. Nikon also fiercely pushes the limits on the megapixel war and usually rates higher on battery life (although I've read that their charging equipment is a bit more clunky). Ergonomically, Canon has a sleeker feel, but again, this depends on personal preference. Canon's starter kit also comes with photo-editing software and Nikon's does not.
The brands use different terminology for certain functions, as well. Shutter Priority mode is listed as "S" on Nikon, but "Tv" on Canon (which stands for "time value"). Nikon also uses the phrase "Continuous Autofocus," which is a bit more clear than the Canon equivalent "Al Servo Autofocus." Overall, Nikon may have less confusing terminology, but the terminology shouldn't be a deciding factor...it's just good to know. Plus, Canon's display screen is preferred by many and it's menu is easier to navigate and requires less steps when changing settings than Nikon.
Lastly, Canon and Nikon handle their lens production quite differently. Canon has a tiered lens system. The highest quality lenses ("L" lenses) are differentiated by a red ring around the lens. Nikon chooses not to apply a tiered system, making all of their lenses equally high quality, no matter the skill-level. Because of this, Nikon's starter lens kit is considered to be better than Canon's, which is lower quality and may need to be upgraded based on your needs. All the lenses from both brands work well though, and your personal preference (yet again) will be what matters most.
In conclusion, every professional photographer has his or her preference, but the truth is, if the camera works and you know how to use it, you're in good hands with either brand. There is no solid answer to, "Which brand is best?" It's all subjective to the user. If you have the privilege, play around with your friends' cameras and discover what features you like. And if you have any other questions, ask away!