Old Man - ZZ Top

Old Marcus Garvey - Burning Spear
Old Man Harlem - Hoagy Carmichael
Old Devil Moon - Jamie Cullum
Old Woman - K's Choice

A Search through my mp3s yields up:

Old Man - Neil Young
Old Man - Randy Newman
Old Kentucky Home - Randy Newman
Old Poe - Lou Reed
Old Dan Tucker - Bruce Springsteen
Old Deuteronomy - Cats (Original Cast Recording)
Old Soul Song - Bright Eyes
Old Woman from Wexford - Clancy Brothers
Old Joe Clark - Dan Zanes
Old Love - Eric Clapton
Old Dirt Road - John Lennon
Old Chunk of Coal - Johnny Cash
Old Brown Shoe - The Beatles

Old Shit / New Shit - Eels
Oldest Story In The World - The Plimsouls

Old Dope Peddler - Tom Lehrer

in addition to a lot of those already listed...
Old Bitch Warrior - Melanie
Old Time Rock and Roll - Bob Seger
Old Folkie - Harry Chapin (tribute to Pete Seger by the same guy who did WOLD)
Old Orchard Beach - The Magnetic Fields
Old School - Danger Doom (from that adult swim collection)
Old Manhattan Melodies - Gary Brooker (singer from Procol Harum, he had one great solo album)
Old Fuck - George Carlin (from his last album and the tour where I saw him live)
Old Man's Advice - Vance Gilbert (blues/folk singer who opened for Carlin and was surprisingly entertaining)
Old Song - AM (from the 2008 SXSW performers collection, no I didn't attend)
Old Dog Trey - Jim Henson as Rowlf (from the album Old Brown Ears Is Back)
Old Compton Street Blues - Al Stewart (pre-Year-of-the-Cat)

my collection includes a lot of very old "Old" oldies like
Old Rivers - Walter Brennan
Old King Tut - Billy Jones & Ernie Hare
Old Cape Cod - Patty Page
Old McDonald Had a Farm - Spike Jones (not just a kiddie song)

and if you include "The Old" or "An Old"...
The Old Apartment - Barenaked Ladies
The Old Lamplighter - The Browns/Kay Kyser/Sammy Kaye (yes, 3 versions)
The Old Philosoper - Eddie Lawrence (classic comedy; you'd know if you heard it)
An Old English Dream - Procol Harum

now, when you get into songs/recordings with Old anywhere in the title, it gets even more fun... My Old School (Steely Dan)... All the Old Showstoppers (The New Pornographers)... The Night They Drove Old Dixie Down (The Band/Joan Baez)... Santa Claus and His Old Lady (Cheech and Chong)... On Top of Old Smokey (The Weavers)... My Old Man (Ian Dury)... My Old Man (The Smothers Brothers, NOT the same song)... My Old Flame (Spike Jones with a singer doing a Peter Lorre imitation)... In Old Mexico (Tom Lehrer)... Good Old Days (Weird Al Yankovic)... Same Old Lang Syne (Dan Fogelberg, don't judge me!)

Old to Begin - Pavement
Old Gray Mare - Tsunami

Same Old Lang Syne (Dan Fogelberg, don't judge me!)

I had ALL of Folgelberg on LP. . .loved him. Saw him a bunch. NEVER listen to any of his stuff anymore.

Old -- Moby
Old Black Dawning -- Frank Black
Old Chunk Of Coal -- Johnny Cash
Old College Try -- The Mountain Goats
Old Devil Moon -- Frank Sinatra
Old Enough -- The Raconteurs
Old Friend -- Shooter Jennings
The Old Gold Shoe -- Lambchop
The Old Main Drag -- The Pogues
Old Man -- Black Lips
Old News -- Dr. Dog
Old Rules -- Hot Water Music
Old Sad Songs -- Lucero
Old School Hollywood -- System of a Down
Old Shit/New Shit -- Eels
Old Shoes (And Picture Postcards) -- Tom Waits
Old Time Lovin' -- Al Green
Old Timer's Disease -- Patterson Hood
Old White Lincoln -- The Gaslight Anthem
Old World -- The Modern Lovers

Old Brown Shoe - The Beatles
Old Fart At Play - Captain Beefheart & His Magic Band
Old Dominion - Essex Green
Old Familiar Way - of Montreal
Old Fools - Magnetic Fields
Old Friend, New Flame - Momus
Old Friends 4 Sale - Prince
Old - Moby

Old Age Pension Blues - Bill Cornett - (Mountain Music of Kentucky)
Old Black Joe - Paulist Choristers of Chicago
Old Black Mattie - RL Burnside
Old Blue - Dink Roberts - (Black Banjo Songsters of North Carolina)
Old Corn Liquor - Dink Roberts - (Black Banjo Songsters of North Carolina)
Old Country Church - Ralph Stanley - (Live in Japan)
Old Country Stomp - Henry Thomas - (Anthology of American Folk Music)
Old Cow Died - Nathan Frazier - (Altamont: Black Stringband Music)
Old Dog Blue - Jim Jackson - (Anthology of American Folk Music)
Old Hen Cackle - Two Poor Boys - (American Primitive Vol. 2)
Old Hen Cackled, laid a Double Egg - Ephraim Carter - (Traveling Through the Jungle - Fife and Drum)
Old Joe Clark - James Crase - (Mountain Music of Kentucky)
Old Joe's Barroom - Dock Boggs - (Folkways Years)
Old King Tut - Jones and Hare
Old Lady & the Devil - Bill & Belle Reed - (Anthology of American Folk Music)
Old Lady Dinah Sitting by the Fire - Ephraim Carter - (Traveling Through the Jungle - Fife and Drum)
Old Leather Britches - Flatt & Scruggs - (Flatt & Scruggs at Carnegie Hall)
Old MacDonald had a Farm - Flatt & Scruggs - (Flatt & Scruggs at Carnegie Hall)
Old Memories Mean Nothing - Del McCoury - (High Lonesome & Blue)
Old Rattler - John Snipes - (Black Banjo Songsters of North Carolina)
Old Reuben - Bill Cornett - (Mountain Music of Kentucky)
Old Sage Friend - Murph Gribble - (Altamont: Black Stringband Music)
Old School Joint - Missy Elliott - (Miss E - So Addictive)
Old Shoes & Leggins - Uncle Eck Dunford - (Anthology of American Folk Music)
Old Smoky - Roscoe Holcomb - (the High Lonesome Sound)
Old Time Pickin' - Ralph Stanley - (Live in Japan)

and this has gotta count, right? ...

Ole Man Trouble - Otis Redding - (Otis Redding Story)

Old Battery - Guided By Voices
Old Dogs - Girl
Old Light - Pase Rock
Old World Lies - Brasstronaut

Old Man Kensey - R.E.M.
Old Boyfriends - One From The Heart soundtrack
Old Blue Jeans - Hannah Montana [you got a problem with that?]

Songs that haven't already been mentioned...

Old Age - Borealis
Old City Bar - Trans-Siberian Orchestra
Old Fashioned Christmas - Frank Sinatra
Old Fashioned Outta Control Loverboy - Q-Unit
Old Friends - Simon and Garfunkle
Old Man - Bret Turner
Old Man Chicago - Alberta Cross
Old Mt. Rudolph - Knight & Doble (& Durgan)
Old New Bicycle - Helvetia
Old Panda Days - Casiotone for the Painfully Alone
Old Pop In An Oak (Rednex)
Old Skool Rocka - Pop Shuvit (2010 SXSW)
Old Suitcase - Easy Anthems
Old Yellow Bricks - Arctic Monkeys
Olden Days - The Channel

Bonus tracks:
Down Home Girl - Old Crow Medicine Show
Poison Control - Old Haunts

Old Dope Peddler- Tom Lehrer
Old Earth, Wash my feet- grampall Jookabox
Old Flame - The Arcade Fire
Old Flames - Harlem Shakes
Old Fools - Magnetic Fields
Old Gold Shoe - Lambchop
Old love - Eric Clapton
Old Man - Leadbelly
Old Man - Neil Young
Old Mother Reagan - violent femmes
Old Mr. Heffer - 4 Non Blondes
Old Orchard Beach - Magnetic fields
Old Photographs - Trembling Blue Stars
Old Riley - Leadbelly
Old Ship of Zion - Leadbelly
Old Shit/New Shit - Eels
Old SOul Song - Bright Eyes
Old White Lincoln - The Gaslight Anthem
Old Whore's Diet - Rufus Wainwright
Old World - Modern Lovers

Actually, that might make a good mix.