I'm running out of slots in my old electrical panel. All of my breakers have a single wire plugged in. Can I free one up by feeding my doorbell low voltage converter into the same circuit breaker that I use for my ceiling lights?
Yes, it's fine to combine circuits onto one breaker, at which point they become one circuit. Provided, of course, that there is not a Code prohibition on that due to certain particular circuits needing to be dedicated, i.e. You can't add anything to a furnace circuit, and cannot add non-bathroom loads to a bathroom receptacle circuit.
Mechanically, you must use breakers listed for your panel by UL. Your breakers might allow 2 wires on a terminal, if not just pigtail them. Wire nuts are allowed in panels.