The earliest commemorative paper money I have owned is a Leith Banking Company one pound note from 1822 that was issued to commemorate the visit of George IV to Scotland that year. The note has a vignette of the royal entourage arriving at port then.
Commemorative banknotes are really more of a modern thing though, think Scotland, Thailand, Mexico that issue a lot of them. They were issued in earlier times but not very often or in large quantities - here is an example of one from Uruguay that commemorated the 100th anniversary of Uruguayan independence in 1930:
This note is now very rare, usually they had their notes printed by Giesecke and Devrient, but this is printed by Banque de France.
Here is a modern note from Tunisia that commemorates an archeology conference in Tunis in 2006:
This note from Thailand commemorates the Queen's 72nd or 6th cycle birthday:
I collect all Thai commemoratives, they are some of the best series in the world.
This Swedish 100 kroner was issued in 2005, and sold at a premium - making it scarce:
Commemorates the anniversary of the founding of Tumba Bruk, the Swedish printer. This note has Svea, a figure representing Sweden since early times.
Mexico has gotten in the act with this 2010 dated 200$00 note commemorating the bicentennial of the independence from Spain:
And then the 100th anniversary of the Mexican Revolution: