Sure you can travel with it and check email if you get the 3G version. It only really connects when it's downloading a new book, you're shopping, or you're checking mail and such. Normally I have my connection off to save battery. I can still read anything I've already downloaded with the connection turned off.
It's all through Wifi. There is a switch on it (on mine at least, not sure how the newer gens work) that you can have it active and it can connect that way. You can turn it off to save battery when you aren't looking for books or DLing things.
I don't know if they have them in the states, but there is also the Kobo. Its pretty much the same thing. My dad has one, and he LOVES it. He can download library books onto it as well, so he hasn't even bought an actual book since he first got it :P
My school has lended me one for the summer since I have a lot of heavy duty summer reading to do for the Helen Ruffin Reading Bowl, and so far it's awesome~ It almost looks like a read page, and it's easy to use. I love being able to change the font and size of the print. On top of that, it's light and portable.