Since my (2012) macbook air has a non-removable battery, and I often just use it at home as a desktop, should I leave it plugged in? Run it off the battery? Is there anything I need to do to maintain it?
Use it on battery once a month until the battery is empty. Apart from that, the battery is good for about 1,000 complete charges. So don't _waste_ charges (wasting charges would be if you sit at your desk, unplug the charger cable, use the MacBook until the battery is empty, then plug in the charger - there are people doing that and it is stupid), but don't worry about it either. 1,000 charges are a complete charge every day for almost three years, or every working day for more than four years. And it's _complete_ charges. Battery down to 50%, charge, down to 50% again, charge again, is only one full charge.
So when at your desk, it's better to have the MacBook plugged into your charger, unplugging it once a month. But no big deal if you don't plug it in sometimes.