Great thread, here are mine:
Banknotes: My oldest are a couple of Assignat notes from the French Revolution; dated 23rd May 1793. My youngest is a 2011 Belarusian 100 Ruble banknote; I've exchanged most of the newer ones worth anything for money to add to my vintage collections.
Smallest note for me is probably a 1920 undated Latvian 50 Kap note; at 54x35mm it beats even my provisional RSFSR notes. Largest would (probably) be my 1943 Victoire 5000 Francs, at 230x125mm. Maybe my 1920 Polish 5000 Marek note is bigger, I don't know.
Stamps: My oldest is a Penny Black from 1840; I've also a Twopenny Blue from the same year, and an unperforated Penny Red from 1841.
No idea about my smallest stamp, but my largest is probably my 1980 London Stamp Exhibition 50p, still in it's original souvenir minisheet.
As you can see, I also like to collect old coins! I'd love to buy some of those Russian coins from either extreme of size someday.... looks like my 1797 George III Cartwheel 2d trumps my 1773 Catherine II 5 Kopecks though, for the heaviest coin in my collection record.
Looks like many people are going to have exonumia as at least one of those records, probably as largest or heaviest; seeing as how medals can go way above and beyond standard coin sizes, what with not having to circulate or anything.