"So I'm thinking of getting a new camera, maybe one of those - what do you call them, the better ones? DSL-somethings? What kind should I get? Nikon or Canon?"
They're called DSLRs.
And it really, truly doesn't matter what brand you get. Oh, and don't forget - Sony and Pentax and Lyca make some fine cameras as well.
Now, if you stopped reading right there, you might suppose, with some puzzlement, that I don't have a preference.
In fact, I have an incredibly strong preference, bordering on blind devotion.
I am a Nikon guy. And I'm a Nikon guy simply because the person who helped me get started in photography was a Nikon guy. Being a Nikon guy, my mentor was naturally better informed about Nikon cameras, lenses, and accessories. I valued his time and advice, and wanted to use what HE used, thinking it would help my learning and discovery process. It did. I can't tell you how many times I called him from the field, stuck, and he was able to tell me just what do, straight from his own memory of his Nikon's buttons and controls.
Notice I haven't said anything about actual image quality. That's because these days, even "low end" DSLR cameras are capable of amazing image quality.
And like my mentor, I stayed with Nikon - starting with that first D70 and moving up to a D80, then a D300, and most recently a D800 - because of the hardware investment. You see, lenses - the most important and expensive proposition for enthusiasts and professional photographers alike - are simply not interchangeable. Not even third-party lenses from manufacturers like Sigma. In fact, Sigma has to produce both Nikon and Canon versions of its entire line.
Now, if you buy a camera body with a cheap kit lens, switching from Nikon to Canon might not be a big deal. But once I handed over my credit card to purchase a nearly $2000 lens - Nikon's much-revered 70-200 f/2.8 VR - I pretty much sealed my fate as a Nikonian (yes, that's the word we use for ourselves. I have no idea what the Canon equivalent is). In that one swipe of plastic, I married Nikon, just as a Mac user with a hefty investment in Mac-only software and accessories is gonna have to stay in the Mac world for a while. Same thing is true of accessories, like flash heads, remote shutter devices, battery packs, and so on. Everything is proprietary. (well, not tripods, bags, and storage cards of course, but you get the idea).
Software is another point of lock-in, although not as critical for some. Nikon and Canon each have their own RAW image formats, each with subtle differences in tone and color and 'knit' as my mentor used to call it. My portfolio has its own style, based on my own custom recipe for image output. Right or wrong, good or bad, it's what I'm used to, and I can post-process hundreds of images like a champ based on my familiarity with my camera's RAW output. Switching to a Canon, with Canon-specific RAW renderings, upsets that apple cart.
So for the person asking "Nikon or Canon?" my answer is the same - it really doesn't matter. Nikon and Canon and Sony and Pentax are in a continual battle, a tug-of-war with each of them trading places as leaders and innovators. Nikon released the D800 and people were amazed. Canon counters with an update to its flagship line that finally gets DSLR video right, and now it's in the lead. Nikon will release a D500, and that will fill a void in its offering. And so goes the dance, on and on. DSLR quality and feature sets advance so quickly that it's nearly impossible to really say who's in the lead at any one given time. Even if one or the other has the lead today, there's no telling how long it will last.
The good news, in my opinion, is that most of the time the consumer wins. Camera technology keeps getting better and better, with costs (relatively) holding the line. Sure, it might take you longer to decide what to purchase, what will all the options and features available, but you're almost guaranteed to get a camera with great image quality and features that blow away models from just 5 years ago (that doesn't guarantee you will take good pictures, of course, but you'll have the capacity to do so).
I can say this for sure: If you're in the market for a new DSLR AND you happen to know me personally, then I'd say go for a Nikon. That way, when you bring it to me because you can't figure something out, only one of us will be confused.