I'd be screwed without my alarm, but I'd be fine other than that.

I have an old iPhone 3G, and I never use it except for Youtube (as it is an old-ass model, none of the other App Store apps are compatible with it) and I most certainly could live without it, as I don't really text people that often.

However my laptop is the one I use for animating and is also the only PC in the house (the rest are Macs) so I really can't do without it.