Seeing as this topic gets started again and again and again in this forum, I thought I would try and give people an idea of what a possible answer to this age-old question is.

First up, there is no answer. Sorry to disappoint you, it's just the way it goes. Both companies are at the top of their game. Neither camera system is better than the other, it is all down to personal preference. I use Nikon digital cameras, and have used Nikon film and Canon digital and film SLRs and I can find no huge difference in the images coming out of them. This is especially the case with consumer level cameras.

I'm going to address the most common comparisons I find here in this forum.

1. Canon vs Nikon
Both Canon and Nikon produce excellent digital SLRs. The way that each company has positioned the cameras in terms of features and price seems to generally alternate, so we start with Nikon D40(x), then Canon 400D, then Nikon D80, then Canon 40D, then Nikon D300, then Canon 5D. Direct comparison between each camera is hard.
The general message is: if you are not locked into a brand already (ie. haven't invested in equipment made by them before), go to a high street shop, get the cameras you are thinking about out from behind the glass and hold them and see which one fits your hand better and where the controls seem more logical. There's no point buying a camera that doesn't fit and whose controls seem illogical (this was the main reason I chose Nikon over Canon, not because of image quality).

2. Canon 400D vs Nikon D40
As said above, direct comparison is a little difficult as they are aimed at slightly different people. The D40 is aimed at very much the beginner. The controls and menus are very simple, and it is also very small. The 400D however, whilst still aimed at beginners, gives a little more room to "grow" into it. Both cameras usually are bought with the 18-55 kit lens, which is generally of bad build quality and acceptable performance. If you are happy with this lens, and don't plan on buying anything else, then I suggest the D40 for its lower price and slightly smaller size. However, the 400D offers a much more compatible upgrade system - any lens that you put on the 400D will autofocus due to Canon's EF design. The Nikon will only autofocus with lenses with autofocus motors in the lens, designated AF-S (or AF-I in older cases). As there is no motor in the camera to drive lenses, lenses designed for this will not give you autofocus. This rules out AF with most of Nikon's fixed focal length (prime) lenses. Whether this is an issue for you is one of personal preference. If you want new Nikon, and you want autofocussing primes, you will need to save up and buy a D80. Otherwise on the second-hand market a D50 or D70 will satisfy your need.
NB. The D40x merely offers 4 extra megapixels, which is of absolutely no use if you only print out at A4 size or below.

3. Canon 1D/1Ds vs Nikon D3 (including is Canon owning Nikon and vise versa)
Once again, neither are directly comparible. All three are professional level camera bodies, built to last and built to do their job. However, the jobs they are designed to do are different. The Canon 1Ds is a full-frame, 21 megapixel, 5fps professional body mainly designed for fine-art, studio and landscape photography. The Canon 1D is an APS-H (1.3x crop), 10mp, 10fps professional body designed for photojournalism and sport. The Nikon D3 is a full-frame, 12mp, 9fps professional body again designed for photojournalism and sport. The only thing in common between the 1Ds and D3 is the full-frame sensor, and that is where the similarities end. The 1D compared to the D3 is more interesting. The 1D and D3 both offer low noise via use of CMOS sensors. The D3 has a higher ISO range (100-25600) than the 1D (50-12800), and from sample images the noise in the 1600-6400 range is slightly better controlled. Both cameras still produce exceptionally clean images at these senstivities, much better than anything film could produce. I would say ISO 12800 from the D3 looks like Fuji 1600 speed colour film, so that's 3 stops better than what was around ten years ago. The only difference really between the cameras is 1 frame per second, a higher resolution on the D3's screen, and a slightly higher resolution on the D3's sensor, oh, and the full frame sensor keeping your wide angle lenses wide. That's pretty much it.

4. Canon Lenses vs Nikon Lenses
Absolutely no difference in quality on normal consumer level cameras. On sensors that can pick out the difference, Nikon generally has better wide angle lenses, whilst Canon generally has better telephotos. This may have been turned on its head however with new lenses being brought out recently by both manufacturers. Either way, both are very good, though do you get what you pay for in terms of image quality and build quality in both ranges. Similar money spent in both ranges will give you the same results, however.

I hope this is some use for people trying to decide between the two brands. Just remember that the biggest factor in making images is you</b, and not the camera or the brand.

--
Oh that is so lame, every hot girl who can aim a camera thinks she’s a photographer
- Stewie Griffin