My desktop (Mac Pro) is almost never off. It does go to sleep/hibernate, but I never explicitly tell it to do so. It'll come out of sleep for incoming ethernet connections.
The reason I do this is now mostly out of habit for a couple of reasons.
First, I hate waiting for a computer to boot. Now that my machines have SSDs and can boot in 8-10 seconds, this isn't so much of an issue.
Second, while in grad school, before the advent of Dropbox or Google drive, I used to store all my work on my own ssh server. This was my way of ensuring I could get to it anywhere in the world. I also ran secure VNC. Of course, the computer had to be on for this to work. So it was.
When I was writing my dissertation, I got Dropbox and Evernote, and they made it ten times easier to just be able to sit at a computer and do my writing, but I was still leery of storing my precious thesis on those services, so I would stil commit all my work to my mercurial server on my home machine.
Even though I have far less use for a home server — my trust in Dropbox and Evernote is pretty high these days — I still occasionally have a need to access my home materials that I don't store in a public cloud. So I have a hole punched into my home network (on a non-standard port) that directly forwards to ssh on my home machine and I still access it.
I do put my laptops to sleep when I'm not using them though.