The first positive thing about a DSLR is that owning one does make you want to explore it's vast capabilities. They are capable of any photography that you've seen, it's more of a matter of what you, the photographer, are capable of. They also perform on a much more consistent level when used by a skilled photographer.
Another positive is interchangeable lenses. The ability to change lenses opens up endless options. It's a double edged sword as it also opens up endless possibilities for spending. For the price of most lenses, you could buy another point and shoot.
The status is nice in some situations too. Just holding a big camera gives you unwarranted clout that can create opportunities mere cheap cameras don't. You can fool them with the cheapest DSLR though. Only other photographers will know the difference.
My DSLR puts me more into a photography state of mind when I take it. If I'm lugging it around, I'm out for the intended purpose of photography. There's something about it's large form factor and heavy weight that just draws more focus to what I'm doing.
The only consistent plus that caused me to keep my DSLR around is the cheapest lens that Canon offers, the nifty-fifty. It's 1.8 f-stop and high quality lens gives a look that I love. It's 50mm size sucks in general because it's really like an 80mm lens on my crop sense 20D, but I've learned to work with it. You can get this look from any DSLR with a quality brand prime lens.
Here is a sample of the look I'm referring to.
|Motorcycle Gas Tank Taken With A 50mm Prime Lens|
Here's the thing though. As professional as this looks, it's just one style of photography. You can get this look with many other zoom lenses, but it's damned expensive! Lesser cameras can still do this style of photography too, they just can't do it consistently with easily predictable results. To me, the trade-offs just aren't worth it to buy the latest DSLR with the plethora of lenses. If my $300 used gear can't make this happen, I'll pass.
In my opinion you absolutely do not need a DSLR. It's just another nice gadget for many types of photography. So long as the price doesn't get in the way, a DSLR will take your photography to another level if you put in the time to learn how to get the most out of them. Don't consider one unless you've used a lesser camera to a point where you're consistently wanting a result that it's just incapable of delivering.
I still carry my convenient point and shoots even when I have the DSLR with me. If you're goal is sports or wildlife photography, be prepared to part with many thousands of dollars for high quality, high zoom lenses that cost as much as a decent used car. The point and shoots cover a range of lenses that most cannot afford so it's an affordable way to get that lens range and adding the 50mm lens/used DSLR combo provides the capabilities for very high quality photos.