I'm an owner of both the iPad2 and the Kindle Fire.
I've spent 1 full day with the Kindle Fire. My thoughts:
Hardware: great form factor, solid feel, and great IPS display.
The lack of physical buttons (except the power button) at first was awkward, but as I used it, was not an issue. I think not including a camera and microphone was a bad choice, but not a deal breaker.
Software: the OS seems nice, but is lacking in configuration options. You cannot currently delete anything from the home screen carousel. (IE: that website you accidentally clicked on now shows up as a huge screenshot on your homescreen!) They will most certainly be fixing this in a software update.
The Cloud integration is great for music, movies, books, apps, etc. And if you are a Prime member, the video streaming and lending library are an awesome bonus.
I've had a few interface issues with tap recognition, and scrolling is a bit clunky (compared to the iPad2), but it's not terrible or anything.
Overall, I'm really enjoying it as an RSS reader, media player (mostly video), email, and web surfing device.
I'm sure the software will evolve to correct the minor issues.
Should you buy it? I think it's a great value for $199.
If you have $499+ and want more features, a better GUI, or have a lot invested in iOS apps-- get an iPad2.
If you have some Amazon Music, e-books, or are a Prime member, get the Kindle Fire (even if you already HAVE an iPad2!).