Not entirely. I'll always "need" a computer. Between the mouse, keyboard, external harddrives, and a larger screen (my 42" HDTV), a cell phone or even a tablet isn't a full substitute for a computer. Plus, there's certain things you can do easily on a computer that are difficult or impossible on a phone/tablet - even things as mundane as viewing certain websites; ads/popups, font formatting, and Flash content can make web browsing extremely frustrating. I have to use 3 different browsers on my phone. I prefer Dolphin because it's fast and formats text properly. But it doesn't support Flash. The stock browser supports Flash, but the controls are clunky. Firefox supports flash, but it does goofy things with text size formatting. I can use Tapatalk, but it doesn't do anything with text sizes or colors. All are a poor substitute for a proper computer with a proper browser.
Even with mass storage (I have a 64gb card in my phone) it doesn't replace the Sansa Clip Zip+ mp3 player I have, because I can clip it to the straps of my backpack, giving me easy access to its controls without having to dig into my pocket while riding my bike. And obviously, when it comes to video (and sound), a 42" HDTV trumps a 4.3" qHD screen.
It hasn't even replaced my digital camera because, outdated though it is, it has features and settings (optical zoom, exposure settings, etc) that a cell phone doesn't. Plus I can't mount my cell phone on a tripod.
That said, the capabilities of a smartphone are simply amazing. If I knew what they'd be able to do now, I probably wouldn't have bought a laptop years ago, but gone with a more powerful desktop like I always have. Even owning a laptop, I might not even bother taking it with me if I were to travel (which I don't do often). I'd just make do with my phone.
I do plan on getting a tablet. I meant to months ago, but I've been holding off for the 2nd gen Nexus 7.