I've found that a lot of DSLR owners end up just sticking with the stock lens. Lenses are really expensive and stock lenses are usually pretty adaptable. For this reason, I've begun to prefer high-end point-and-shoots like the Powershot G16; it has many more features and much better processing abilities than my old Digital Rebel, and since realistically I'm not going to lug around the DSLR and 5+ lenses for any situation that may arise, I've found P&S cameras to be much more convenient and very versatile.
I would only use my DSLR if I knew I would need to photograph some circumstance that my P&S couldn't handle. I know this makes me a black sheep within the photography community and there are lots of people who like to make fun of me for it, but the reality is that unless you're trying to get a specific shot, a versatile, general-purpose lens is all you take with you on your DSLR anyway, and you're better off using the lighter, smaller, cheaper P&S.
For the vast majority of low end DSLR shooters, buying a fast prime lense (eg. 35mm 1.8 for 1.5x smaller sensor) will have the biggest single impact on their photography. It gives them much more headroom in low light and much shallower DoF for portraits.
It's also much smaller and lighter than the chunky 18-55 the camera probably comes with.
I can't upvote this enough. The owner of something old like an EOS 10D would be far better served investing $1000 better glass than they would upgrading their body. I purchased the Canon EF 50mm f/1.4 USM for my EOS 10D ($400), and spent the next two years taking completely new pictures. The pictures that I took with my EOS 7D didn't look that much different from the EOS 10D (though the faster focus and startup was greatly appreciated)
The only problem with a fast prime lens is that it can be "too fast" - i.e., super shallow DoF (e.g.: in a portrait, parts of the face are in focus while others are already seeing bokeh).
The Canon 50mm 1.4 is in this range - you need to be very good to avoid the super-sharp DoF.
Personally, the best benefit of a DSLR is the external (bouncable) flash. That's something that smartphones aren't going to solve anytime soon.
Who are these people who regularly take photos at f1.8? At least with a full-frame sensor you'd almost always want more depth of field that that. Having a super-wide aperture may be an indicator of lens quality but it's not all that much use in itself.
I loved the pictures I could take with my f1.4 - particularly macro photography, insects, flowers, etc.. but also low-light portrait photography. The f1.4 lets in a ton of light, and shoots really fast, so you can get a low-light portrait with great bokeh. The second best lens I ever purchased for my camera was the Canon EF 50mm f1.4 USM.
Bokeh is kind of subjective, so I won't argue that. If you're not using full frame then maybe having some wider apertures is useful for that, but I would think you'd almost always want more depth of field than f1.4 would give you.
Apart from that, you're only letting in around three more stops of light than a kit lens and half a stop more than a cheap 50mm prime. You can almost always work around that with some combination of (i) underexposing, (ii) using a slower shutter speed and (iii) bumping up the ISO.
People used to say the same things about f1.4 lenses before digital, but the fact is that shooting at ISO 800 you can get the same overall sensitivity/quality balance at f4 with a digital camera that you could at f1.4 with a film camera.
If you spend all your time trying to shoot fast moving completely-flat things in the dark -- and you can somehow focus fast enough at f1.4 -- then maybe f1.4 is useful, but that isn't representative of most photography.
I was about to write this same thing. For $200 you can get either the Nikon or Cannon version of the 35mm and greatly improve every picture you take. It also opens up a lot of artistic options with DoF and lighting.
I would only use my DSLR if I knew I would need to photograph some circumstance that my P&S couldn't handle. I know this makes me a black sheep within the photography community and there are lots of people who like to make fun of me for it, but the reality is that unless you're trying to get a specific shot, a versatile, general-purpose lens is all you take with you on your DSLR anyway, and you're better off using the lighter, smaller, cheaper P&S.