The good news is, there are some unreleased Hum songs out there.

The bad news is, given Hum's track record at releasing albums and songs, chances are slim that we may ever get to hear and experience any of the aforementioned material.

Pre Fillet Show  -  A 10 (?) song demo was supposedly recorded with engineer Steve Albini. It is extremely doubtful we will ever get to hear this

DIH  -  Mark Rubel (DIH producer) has hinted that there are some unrealeased songs and / or outtakes from the DIH sessions at Pogo Studios. Hopefully the band and RCA will give permission to release these someday, perhaps as B-side fodder. Of course it is equally possible that Keith Cleversley (YPAA producer) might have similar material as well, though there has never been any mention of it. Who knows? Maybe Brad Wood (E2K producer) has some unearthed Hum material.

Covers  -  Hum has been known to perform a cover of The Police's 'Invisible Sun'. In fact, they were originally scheduled to record it at Pogo Studio (and may have completed it) for the soundtrack to the 1998 movie X-Files: Fight the Future. Unfortunately, Sting swooped in at the last minute and decided to do a reggae version of the song instead, thusly replacing Hum.  We'll never know how much exposure Hum was unfairly cheated out of because of this. Their response? "Fuck Sting."

Post Downward Is Heavenward  -  Several  tracks were recorded by Hum in their own home studios (read: basements) with, possibly, a Roland VS-880. The exact number of songs and their official titles are unknown. Rumor has it that they are currently residing on Jeff's hard drive. However, a few fans have managed to catch glimpses of set lists from recent shows that drop clues as to the what the titles are or will be. Here are a few in no particular order:

    Inklings  -  check out HUM.N3.NET for a live sound clip of Inklings (full length, but poor quality)
    Cloud City  -  Star Wars / Empire setting / theme? Possibly converted to a Centaur song (Matt's new band)
    Power
    New Pop One
    Hip Hop
    Jeff's fast
    Jeff's 3/4
    Creepy
    Frozen Style
    Jungle Boogie

It is interesting to note that the song 'Inklings' was inspired by the mythical sub-terranian, acoustic-responsive creatures called INKlings, in Haruki Murakami's book, Hard-Boiled Wonderland and the End of the World. Below are the tentative lyrics for 'Inklings' courtesy of DK:

Inklings

Up on the stairway sulking, now
The inklings have left me with no place, not a sound
*
Let's be together
Let's be forever
Crush the inklings on our spines
*
Let's be together
Let's be forever
Kill the inklings in our minds
*
Up on the stairway sulking, now
The inklings have left me with no place, not a sound
*
(?) Strap on srginrpenrv(?), love-laced now
Father of brixonst and stixonst, how
*
Let's be together
Let's be forever
Crush the inklings on our spines (crushing inklings on our spines)