I play mostly my own songs. But I've built up quite a few covers and traditionals over the past year.

On the 5-string open-back banjo:

Paint It Black – the Rolling Stones
Willie of the Winsbury (trad)
Ballad of the Bollweevil (using Mance Lipscombe's melody, which sounds a bit like Frankie & Johnny and unlike any other 'Bollweevil' I've ever heard)
Dear Prudence (the Beatles)
(the above all lend themselves well to C tuning)
Darling Corey
In The Pines (sort of a hybrid version between Leadbelly's 'Black Girl' and Bill Monroe's version)

On resonator mandolin:

St James Infirmary
Sometimes I feel like a motherless child
Hand Me Down my Walking Cane (with the lyrics changed to excise all the religious stuff and make it exclusively about getting wasted on various different alcoholic beverages)
(all directly inspired by the excellent Dix Bruce "Teach Yourself" book, which I can thoroughly recommend)
Germ Free Adolescents by X-Ray Spex

On acoustic guitar:

Brisk Young Widow (version based on the arrangement in a book of Cecil Sharp transcribed for guitar I found in Brixton library)
Parachute Woman by the Rolling Stones
I Need Somebody by the Stooges
Dum Dum Boys by the Stooges
No-one Knows by Queens of the Stone Age

On charango:

Theme from The Flumps