tl;dr: The iPhone 3G is a great upgrade from the 1st generation iPhone, but suffers from a sluggish processor and a limited lifespan.
This iPhone review will be expanded upon in the coming months, and will grow with time—if you've ever used an iPhone, you'll know why: the thing just keeps giving more and more surprises with more use!
The Hardware
I've used the first generation iPod Touch, the first generation iPhone, and various 'smartphone' models from other manufacturers, including Palm, RIM, etc. The iPhone/iPod have something that the other models are almost always severely lacking: gripability. My hand simply seems attracted to it! It's the same way with the old iPod mini (which was, in my opinion, the most holdable electronic device ever).
The buttons are sensible, if a little too hard to press. The power button on top isn't always as easy to hold down for a power-down, or to turn on the iPhone. The volume buttons on the side are pressed accidentally from time to time, but I'm okay with that - it doesn't happen too often. The silent switch on the side is the most oft-used button on the device for me, since I'm in and out of meetings and quiet places quite often, and it works beautifully.
Plugging in the headphones (something I rarely do, since I have an iPod shuffle for running, etc.) isn't any problem, nor is plugging in the dock cable. Some iPod models from the past seemed harder to stick cables into, but the iPhone is perfectly acceptable in this regard.
During intense use (a 40+ minute phone call, or a 20+ minute web browsing or gaming session), the iPhone's back gets noticeably hotter, and, while not painful, it can be annoying to hold. Also, speaking of holding the iPhone, you'd better invest in a couple microfiber cloths to clean the thing every now and then. Finger prints stay on the back until you clean them off. The screen's usually okay, unless you're eating greasy popcorn or White Castle® food.
Other than that, I can't think of anything hardware-wise that would hold someone from buying the iPhone. It's great!
The Software
The iPhone's OS is the one-and-only reason why the iPhone has succeeded over other smart phones, and the reason why people lust after the iPhone. The user interface is drop-dead simple; my little sister figured out how to find a game she wanted to play and start playing it within seconds. Heck, my Mom would actually know how to add a phone number to the address book (something she'd rather not figure out on her flip-phone!).
You can read reviews of individual apps and software elsewhere—I'm not going to go into them. I'll just say that the iPhone's software rarely stymies my ability to do most of the tasks that I used to lug my laptop around with me to accomplish.
I can check and reply to emails (connecting with my office's Exchange server is a breeze, too!), schedule appointments, text, browse my news feeds (I use NetNewsWire), navigate to addresses via the 'Maps' app, check Facebook and Twitter, and do anything but tasks like post full blog posts or edit images. While there are rudimentary apps to do almost anything I can do on my Mac, it's not worth my time to sit at my iPhone pecking away a 500-word story or retouching an image for the web!
The Future
Apple has announced that its 3.0 software update for the iPhone will include many features users have been begging for, including copy and paste, MMS, push notifications, and in-app purchases... to tell the truth, I haven't really needed to use any of those features (with the exception of the occasional copy/paste), so I could almost care less. But anything that allows more people to hop on the iPhone bandwagon is fine by me.
AT&T
I would be remiss to neglect mentioning the only carrier in the US who has the iPhone. AT&T's service in most of the Midwest is actually pretty good, and their rates are comparable with other carriers' smartphone + data access rates. The only sticking point I have is that I'm paying an extra $5/month for 200 SMS messages. You'd think that if you have unlimited data, AT&T could figure out a way for your phone to send and receive SMS freely over the data package.
But, no. Phone carriers are phone carriers. Whether you're using Verizon, Sprint, Alltel or whoever, you're getting gypped. Deal with it.
Jailbreak!
I jailbroke my iPhone a few weeks ago for the sole purpose of getting 3G WiFi access using the excellent little PDANet app from time to time. I've only used this service maybe once or twice, but having it was well worth the cost of PDANet and crossing my fingers during the jailbreak process. (If your iPhone has problems because of a jailbreak, well... you're screwed).
If you jailbreak your iPhone, you can do a ton of other things, too... like having a moving background on your home screen, or customizing your icons. But I don't really care about that—and I care about my iPhone's battery life.
I would only recommend jailbreaking your iPhone if you have a little technical ability, and if you are a risk-taking person. Otherwise, wait until 3.0 comes out, and see if there are new apps or functionality that will let you do what you would like on your iPhone without jailbreaking!
The iPhone 3G cost $200 with a contract new, but you can find it used and without a contract for under $100 nowadays.