My logic in picking these songs was as follows:

1. Covers many people would recognize but that have (mostly) not been
overplayed on the radio or by other bands;
2. Singable, usually if transposed into another key but some would work
in the original keys;
3. Variety of lyric themes ("Whipping Post" is too negative, but there's
nothing wrong with sad songs; I tried to put in some sexy stuff 'cause I
remember how much Phil enjoyed singing "Why Don't We Do It In The Road?");
4. Interesting musical potential (for jams, of course, but also if the
guys want to slip in something quick and upbeat, like the Dead used to
do with "Me & My Uncle").

OK, here they are, by artist. Obviously many are pop throwaways. I
marked the ones I feel most strongly about with an asterisk. About 20 of
them were suggested by my husband.

Allman Brothers
 *Dreams
 Every Hungry Woman
 In Memory of Elizabeth Reed

Average White Band
 *Pick Up The Pieces

The Band
 Jawbone
 Don't Do It
 Daniel & the Sacred Harp
 *Life is a Carnival
 When You Awake
 Endless Highway

Beach Boys
 Long Promised Road
 Do It Again
 Do You Wanna Dance? (for Jerry--everybody and their kid sister
  have covered this, obviously)

Beatles
 Things We Said Today
 Across the Universe
 Ticket to Ride
 *Taxman
 While My Guitar Gently Weeps
 *Hey Bulldog
 With a Little Help From My Friends
 *Drive My Car
 Sun King-->The End (2d side of Abbey Road, minus first track)

Blood, Sweat and Tears
 Something Going On
 Meaghan's Gypsy Eyes

David Bowie
 Ziggy Stardust
 All the Young Dudes
 Suffragette City

Jackson Browne
 Redneck Friend

Byrds
 So You Wanna Be a Rock and Roll Star

Beefheart
 Hothead
 *Advance Romance

Chambers Brothers
 Time

Chicago (medley)
 Does Anybody Really Know What Time It Is?
 Beginnings
 Questions 67 & 68

Joe Cocker
 Feelin' Alright
 *Sandpaper Cadillac

Elvis Costello
 RadioRadio

Cream
 Badge
 Sunshine of Your Love
 *Strange Brew
 White Room

Deep Purple
 Hush

Dire Straits
 Down to the Waterline
 Water of Love
 Skateaway
 Once Upon a Time in the West

Doors
 *Roadhouse Blues
 Unknown Soldier
 Wild Child

Derek & the Dominoes
 *Anyday

Peter Gabriel
 *Sledgehammer
 Salisbury Hill

Jimi Hendrix
 Voodoo Chile/Slight Return
 The Wind Cries Mary
 *Red House
 Little Wing
 EXP

Jefferson Airplane
 *Crown of Creation

Elton John
 *Holiday Inn

Kinks (medley)
 You Really Got Me
 Tired of Waiting
 Sunny Afternoon

King Krimson
 *In the Court of the Crimson King

Led Zeppelin
 Misty Mountain Hop
 *No Quarter
 Dazed and Confused

Bob Marley
 *Waitin' For My Baby
 Is This Love?
 Soul Shakedown Party
 *Mellow Mood

Steve Miller
 Jet Airliner

Moody Blues
 Afternoon (Tuesday?)
 Story in Your Eyes

Van Morrison
 *Sweet Thing
 Astral Weeks

New Riders
 ****Garden of Eden**** (I thought the Dead were nuts for not doing this!)

The Police
 Demolition Man
 Too Much Information
 Does Everyone Stare?

Lou Reed
 Walk on the Wild Side
 Dirty Boulevard

REM
 *What's the Frequency, Kenneth?

Rolling Stones
 *Torn and Frayed
 *Jig-Saw Puzzle
 Rip This Joint
 Silver Train
 Winter
 Sway
 Dead Flowers
 Til the Next Goodbye

Todd Rundgren
 Dust in the Wind

Bob Seger
 Fire Down Below

Steven Stills
 Love the One You're With
 Change Partners
with Manassas
 The Treasure

Talking Heads
 And She Was
 City of Dreams
 Big Country
 *Heaven
 People Like Us

Richard Thompson (some of these were recorded with Fairport Convention)
 *Wall of Death
 *Genesis Hall
 *When the Spell is Broken
 *Calvary Cross
 *John the Gun
 *Now Be Thankful
 *Sloth

The Who
 *Bargain
 *Substitute
 Magic Bus
 Goin' Mobile
 *Gettin' In Tune

Neil Young
 Barstool Blues
  Human Highway
 *Cortez the Killer