Oh no, you've opened a real can of worms!
Really, you need two cameras. A pocket point-and-shoot that you can just take anywhere. If you're using an iPhone, then you've got that built in already. Take a look at the photos people are getting with iPhones:
http://www.flickr.com/groups/takenwithiphone/pool/ If that doesn't suffice, or you find yourself being limited by your camera's feature set, then you should probably consider diving into the DSLR market. If you're on a super tight budget (under $500), then you may want to looking into buying a used Nikon D70 or a Canon Digital Rebel (depending on your preference). You can find them on Craigslist.org with a lens in great condition for $400 +/- if you just have a little patience. You don't want to end up with something that's been abused or stolen. Photographers are habitual upgraders, so there's a lot of great used gear out there.
If you've got more cash burning a hole in your pocket, then you're coming into this world of digital SLRs at a fantastic time. Both Nikon (my preference) and Canon (really just as good) have some great entry level and semi-pro DSLRs that are totally fantastic and can be had at what I think are reasonable prices. These are the Porsches 914s of the Camera world, so there may be a little learning curve with some models (though some are suprisingly automatic).
Off the top of my head, here's what I recommend. I'm sticking with Nikon and Canon, as though are the only DSLRs I really know anything about:
- Nikon D40X: Nikon's Entry Level DSLR, 10.2 Megapixels, you have to use Nikon DX Lenses if you want auto-focus. I've found new, non-graymarket (don't buy graymarket!) kits (body, lens, memory) for $600.
- Nkon D80: Nikon's next step up from the D40X. Also 10.2 MegaPixels, but more features and you have more lens choices. Better performance all round. Kits (body, lens, memory) for around $1k
- Canon Digial Rebel XTi: 10.1 MegaPixels, better low light performance than the entry level Nikons. My gripe is that they're made of plastic, so they feel a little toy-like to me. I'm also not a big fan of Canon's entry-level lenses for the same reasons. However, this camera takes awesome photos and it's priced around the same as the Nikon D40X
- Canon EOS 40D: New, 10 MegaPixel, Semi-Pro for a great price (around $1500 in kit form). I don't know a whole lot about it, but I'm sure it's awesome.
- Nikon D300: Nikon's new 12.3 MegaPixel camera. Better low light performance than the D200, huge LCD on the back with Live View and 640 x 480 resolution, semi-pro, good for studio and field work. You'll be out 2k smackaroos for a kit.
Nikon and Canon have also both released new top of the line, pro cameras. But if you're that serious about photography, then you already new that. Just the bodies alone will set you back over $5,000 and because they're full frame, you'll probably need to replace your lenses as well to get the full benifits that each has to offer.
If that's still not good enough, then you can go spend $40k on a nice 40 MegaPixel medium format Hasselblad digial camera. All the cool kids have those.
I have to also recommend that you invest in a nice shoe-mount flash if you plan on doing any indoor, low light photography. Being able to bounce light off of the ceiling or the wall is a million times more natural looking than firing straight at the subject. The results are the difference between a mug shot and... um, something nice to look at.
I've been shooting with a D200 for the past six months or so, and I'm in love. The D300 would be on my wish list, but it's not a big enough of a step up, and then next step up would set me out of pocket at least $5k (not including glass). I shoot with a 18 - 70 mm lens most of the time, but prefer the image quality of my 50mm f/1.8 prime lens. It's cheap, shoots super fast and is great in low light. You can also get some pretty extreme DOF effects with it as well. I have a lousy 70 - 300 for the long shots, but it's not very sharp. I've borrowed macro lenses and I can't get enough. Currently looking at the Sigma 150mm macro lens and it will probably be my next big purchase.
I have lots of favs, but I don't want to use up too much space here.