The longest continuing daily tradition in the world (and consequently, one of the longest on-going positions) belongs to a horn-player.
The night watch has been set in Ripon, North Yorkshire, by the Hornblower at 9 PM every night without fail since the year 886. As the story goes, Alfred the Great visited Ripon and was so impressed he granted the city a Royal Charter. As he had no document prepared, he gave the citizens a horn to seal the deal, and advised them to be ever vigilant against the Viking hordes which were quite a nuisance at that time. The citizens heeded this good advice and appointed a Wakeman to keep watch through the night. The Wakeman was to blow the horn to alert that he was now on duty and all was well.
This ritual continued until the year 1604 when it was decided the Wakemen had become too abusive and powerful, and the city elected a Mayor instead. The Mayor appointed the Hornblower to continue the tradition, but to report to him (the Mayor) that he (the Hornblower) had actually carried out his duties. Thus, the Hornblower today must, after carrying out his hornblowing duties on the town square, seek out the Mayor wherever he is, and report that all is well by blowing his horn for the Mayor as well.
The Hornblower in early 1930's
This link has interesting info and photos, and I also enjoyed this video below.