I had a dead bulb in a recessed ceiling can, and upon screwing it out, the neck of the bulb broke off and it sparked, tripping the breaker. I removed the rest of the bulb from the socket and put in a new bulb and now none of the 8 bulbs that were on that switch work (of course I reset the breaker). There is no evidence of burning within the fixture. Does anyone have any ideas of how I can fix this? I tried several different bulbs, but don't think it is the bulb as none of them light now.

What happens sometimes is the short circuit causes a loose or weak connection someplace in the circuit to open due to the high current that flows during a short circuit.

All I can suggest is to start at the circuit breaker, be sure that breaker is working, and trace the circuit, open each junction box, fixture, etc, checking the connection in each looking for the poor connection, either splice, or terminal.

As an addendum to T.K.'s response.

Please check all of the bulbs that were not changed. Sometimes the short will take out all of the other bulbs.