I've got the first generation MBA, with the 80GB hard drive. I use it for travel, go on holiday with it (it went to Canada last year) and when it's too hot to use my Mac Pro (which puts out a lot of heat). For non-intensive tasks, it's great. I'd hesitate to run something like Aperture with tens of thousands of photos or a Windows VM, but that may have changed in the newer models.
I'm not sure I'd want it as my sole computer, though. Like others have said, its expandability isn't great: one USB, a headphone socket and a mini DVI slot. If I plug my first generation iPod shuffle in, I can't use the headphones (!). You also don't get an internal DVD/CD drive and you can only have 2GB of memory.
The reason I bought mine was mainly down to the size and weight. I wanted something that I could lug around all day in a bag with a load of camera equipment. I thought both the MB and MBP were too heavy and I much prefer the looks of the Air. And I didn't need a top of the range laptop - I've already got a tower for the heavy stuff. Other than size and weight, other positives: it's quiet, the screen is fantastic and the keyboard is lovely.
I certainly wouldn't recommend against buying a MBA. But you should be aware that it isn't perfect by any shot. The best thing you can do is to go to your local Apple Store or retailer and try one out. Then try out the other laptops and see how they compare.