Wellll… I leave my work computer and home computer on all the time.
Usually in the side bar I see a Shared(?) column that shows connected computers. I've made VNC 'aliases' and usually just click on them to Screen Share.
I have lots of work to do at home, but nuthin' is there, and I can't connect.
I walked back to work, and sure enough, I can Screen Share my home computer. Walk back home, and nada.
I rebooted, turned Airport on and off, restarted modem…
One of things I've never figured out (#34,769), is when I open Screen Sharing, a window comes up asking me to 'Connect to Shared Computer', and I'm supposed to type in something where it says 'Host'.
Never had to do it, and don't know what I'm supposed to type in there… after all these years.