I love my books, so I was amazed at how much I also love my Kindle. Here are the pros for me:
Comfort - the kindle is light and comfortable to hold. I have mine in a cover so that I can hold it like a book. It is fabulous for fat, heavy books like Wolf Hall. And I can hold it in one hand if standing on the train.
Easy on the eyes - I would agree that you should go for an e-ink version and definitely not a glass screen or anything back lit. Back lighting cause sleep disturbance if you are reading before going to bed and glass causes glare, making it hard to read in even the mildest of outdoor light. Being able to increase the font size is a huge boon when you realise you've forgotten your glasses. Again. I find the reading experience very pleasant indeed, almost easier than print with my dodgy middle-aged eyes.
Increase your vocabulary! - Click and highlight a word and you get instant access to its definition. If you get the 3G version (which I'd also recommend) you can go online to research things further.
Instant access to books: Almost instant download over wifi and 3G. There is no contract or cost with the 3G, above and beyond your purchase price.
Sync between devices - you can download Kindle apps for iPhone, iPad, PC and (I think) Mac. You can bookmark where you are in your book in any device, pick up another device, sync and it automatically takes you to where you left off. Great if, for example, you forget your Kindle but you have your iPhone in your pocket.
Now that I've settled in to using my Kindle, I actually prefer e-books and get a bit grumbly if I have to read a paper book.