In the literal sense, I could live without any gadgets (I'm not in the ICU, y'know - and saying I'd die if I didn't have a convenience gadget is a bit melodramatic).
However, what would be a major hassle for me to give up? A laptop + smartphone with mobile broadband. Having the internet almost anywhere is too great of a convenience, especially when trying to buy computer cables. (Go ahead and compare a DVI to HDMI cable at any brick and mortar store to one you can find online and tell me that $60/month internet doesn't pay for itself!) The internet is great - newspapers, shopping, books, radio, TV, mail, photo exchange, and so much more 24/7!