I have a Sony Reader and really enjoy it. There are both advantages and disadvantages to it.
*Easier to travel with -- can take multiple books on a vacation and it doesn't take up any space in your luggage
*You can read easier while you eat or do other things because you don't have to hold the book open (my husband likes to read it while he shaves)
*Better for people with allergies -- less accumulation of dust (I definitely have this problem. I love my paper books, but they do get dusty)
*Privacy -- No one can see what you're reading, so you can read whatever questionable book you want!
*It takes getting used to not reading a paper book
*You can't read while a plane is taking off or landing
*If you have only one reader and are traveling, your significant other or someone else will often ask if they can use it when you want to!
*There is always the chance of it getting broken or stolen -- that's a way more expensive loss than a paper book for the most part
I have to say that I read my fair share of paper books, but I also use my reader quite a bit. I would say that e-book readers are INVALUABLE while traveling. I have left books in hotels because I didn't want to carry around the bulk after I finish reading them. It also gives you less space in your luggage when you carry multiple books with you. If you travel a lot, I would definitely recommend getting one just to lighten your load.