I’ve got a Kindle.  It usually gets stuffed into a pocket in my backpack, or stuffed into a pocket in my camera bag (with the camera and lenses inside pressing against it through the main pocket).  I’ve dropped it a few times, and I’ve had to clean droplets of spilled coffee/ramen broth/whatever off of it from time to time.
So far, I’ve had part of the casing on one corner pop out of place (popped it back into place), and the “Next” button on the right side feels a bit loose (there’s a spare on the other side if it ever breaks completely).
Also, if you use the 3G wireless option in Japan, it eats up the battery like crazy.  Not sure why.  I don’t normally need that option, so the wireless is kept off most of the time.
It’s not a very good web browsing device compared to my iPod Touch, but it’s a pretty danged good one considering that web browsing is not a feature on it that they advertise (from what I understand, they quietly disabled it for the Kindle Touch due to data costs for them).  It’s listed in the menu under “Experimental” and is a bit inconvenient to get to.  I have used it in the past to get to Facebook and Gmail’s mobile webpages, which has been a lifesaver when letting my wife know I had arrived at the airport when flying home from Korea (my Korean pre-paid cell phone did not work in the US, and my wife could receive emails on her phone).
That said, one of Facebook’s updates included changing how the Notifications menu works, making that particular function not work very well on the Kindle for some reason.
If you spend $180 on an eReader, why not go all out and spend another $20-50 for a case to keep it in?  Amazon offers one for the Kindle for $60 that’s available in multiple colors and includes a reading light (which would have been handy for me on those late-Sunday-night bus rides back to base on the Air Force-owned buses that invariably had the ceiling lights disabled for some reason.  I once actually ended up using my iPod as a light to let me read my Kindle.
Book cost-wise, it varies.  From what I understand, the costs on the Kindle store are often set by the publishers (if Amazon doesn’t want to sell that eBook for $9.99, they can feel free not to sell that eBook at all and let their customers go to the Barnes and Noble eBookstore to spend $9.99 on it instead).
Nobody has mentioned it here, but one meme I usually encounter in these discussions is the claim that you HAVE to buy eBooks from Amazon’s Kindle Store.  It’s pretty clear that folks in this thread know that’s not the case, so I can only assume that the SDMB’s fight against ignorance has made a bit more progress.  Many of the books I read are published by Baen Books, and they offer many of their books on Webscriptions.net typically for around $6.00.   You can get advanced copies of books before they hit the streets for around $15.00, but I understand those include typos and such as a bonus.  They also sell bundles of books at a discount.
Some online bookstores that sell books for the Kindle (usually in Mobi format) can deliver them electronically if your Kindle is on a wifi connection, using your Kindle’s email address (both Amazon and Webscriptions have pages explaining how to set this up).  The Kindle’s email uses a Whitelist which only includes Amazon by default, in order to keep folks from dropping stuff on your Kindle against your wishes.  If all else fails, download the book to your hard drive and transfer it via USB cable.  If you forget your USB cable, duck into an electronics store or a Wal Mart if you have time, and grab another one (the Kindle uses the Micro-B USB plug, which is also pretty typical of many cell phones I’ve seen in the past few years.
As far as a Dead Tree Book not requiring power, try reading one at night some time.  They don’t work very well at all without power in those circumstances. 