Ubuntu is clearly taking the lead in this race. However, I am not sure this is the right approach to mobile/ubiquitous computing b/c phones brake, discharge or are lost/stolen. The best approach in my personal experience is to have terminals that connect to cloud computing services. The phone too can connect to the cloud in case a quick on the go edit/reply/action is needed. In this regard, current services already fill such need, Android and Google web apps for example. In other words, if you need to add all peripherals (screen, mouse, kb) and you most likely will also use the local LAN/WiFi (lower cost+ higher speed), then might as well add another CPU to that mix and don't depend on the phone.
There is another side to this. With "cloud" you trust remote party to process the data for you. With the mobile, you trust the local device. Even if the cloud means "an audited software, which you run on hardware you physically own, located at your housing" (which is rarely the case) I think it's still less safe than a device that does everything right in your hands.
I've had something close to this for years with my N900 (circa 2009). It detects when I am at home or work (via WIFI), and mounts its file systems on my laptops via sshfs. I can run Debian apps on my N900, and have the laptop display the UI via X11. I'm hoping this will work even more smoothly when I get my neo900.
Is there anything stopping you doing this on current Android devices? You can run a debian userland without any trouble, and there's an X11 server available in the Play store (`x.org.server`).
I suppose the usability leaves something to be desired in the general case, but even all-in-one apks like `org.gimp.inkscape` go a long way to addressing this.
I've been yammering about something like that for ages: I want to arrive at my desk, place the phone by the screen and start working as I would on my laptop. However, I want this with my Linux desktop loaded up, not my Android one. Ubuntu did almost nail with the initial videos of Ubuntu phone but I never seen it take off.
This sort of thing seems like it has interesting uses, but I doubt it will become mainstream.
Assuming your mobile device has adequate horsepower to run your desktop, the marginal cost of adding equivalent CPU, RAM and storage to the monitor you'd need on your desk, trends lower and lower every year, and is already pretty low.
Blackberry's OS10 phones do a solid job providing this feature. HDMI out to a larger screen, bluetooth connected keyboard and mouse. They also have their Blend software for Windows/OSX which is somewhat the reverse, use your phone without actually using your phone.
A few years back, someone (I can't recall the source) was prophesying Apple making a "laptop" that behaves like this, leveraging your iPhone's CPU. Basically a MacBook Air without the "computer".