Having several friends who own SLRs, I actually have to say having seen them use theirs steered me away from buying one, and instead I went for a high-end compact one. Problem with SLRs is that they are so damn clunky, and if you want to use their range, you find yourself lugging around several lenses.
Compacts are more versatile, and in fact one of those friends bought one not too long ago, and has been using it exclusively now.
There's definitely something to be said for this, and as good as compacts have gotten it's a damn fine approach. Myself, I actually enjoy the tinkering aspect a great deal (despite being not very good at it). To me it's more of an interesting hobby than a means of capturing experiences. A modern DSL can give you as little or as much control as you want over what you're doing. That's why I went the DSLR route when planning my trip to Europe. I usually take a compromise approach myself, where I'll shoot in shutter or aperture priority mode, depending on what I'm looking for, and let it handle the math. At the same time I can switch to manual mode and be left completely on my own, or auto mode and treat it as a good quality point and click. Best of all worlds, honestly.
While it does mean toting a bag around for a short and long lens, I've gotten pretty good at it over the years, and it offers up some advantages anyway. With just a compact you're not carrying around anything but the camera. It's nice to have the manual with you. I've also got some cleaning gear, extra battery and ziplock bags which have come in very useful when I get caught in rain. Stuff that would be at home in a drawer if you didn't have the bag.
Metty, if you decide to go the DSLR route, consider Olympus. Things might have changed, but traditionally they're a great compromise option. You're not going to get Nikon optics, they are the gold standard after all, but they'll be very good anyway and you'll get more features for the price.