My phone, sure I could go a week without it. Heck, it's out of minutes as I type (wish they would hurry up and send my taxes though).... Now, if your question had been "can you go a week without using the computer", that would be totally different! I can go with minimal use of a computer, but not for a whole week. After all I have to check multiple email accounts, being a freelance web designer makes it even harder, and of course my social networking addictions.
I love my desktop when I'm home, laptop for road trips, now if only I had a computer in the glove department of my car I'd be in Nerdvana! lol