These are songs that were played briefly ('teased') by Jane's. They didn't play the full songs, just a little of them.. ranging from a few seconds to about a minute or two.. like between songs, kind of as a joke or to make sure they were in tune, or for fun at soundcheck, or just for the hell of it.
I'm sure I'm leaving out a bunch, but here's some I know of...

--song-------artist------known occurrence of jane's doing it---
A Forest - the Cure
A God in an Alcove - Bauhaus
Bali Eyes - Porno For Pyros (Auburn Hills, MI 10/20/01)
Beat It - Michael Jackson (many times in '87)
The Beautiful People - Marilyn Manson (once on '97 tour)
China Cat Sunflower - Grateful Dead (soundcheck, L.A. 4/25/89)
Communication Breakdown - Led Zeppelin
Day Tripper - The Beatles (Nottingham, London 3/12/91)
Dazed and Confused - Led Zeppelin (a few times)
Foxy Lady - Jimi Hendrix (Glasgow, Scotland 8/25/02)
Gallows Pole - Led Zeppelin (Vancouver 11/3/01)
Get It On - T. Rex (sometimes during 3 Days)
Hava Nagila - traditional (sometimes during Chip Away in '97)
Helter Skelter - The Beatles (Mountain View, CA 10/26/01)
Hey Joe - Jimi Hendrix (Seattle, WA 11/7/01)
I Don't Know - Ozzy Osbourne (Dave and Steve at soundcheck 10/23/08)
I Wanna Be Your Dog - Iggy & The Stooges
In The Flesh - Pink Floyd (several shows in 2002)
King Volcano - Bauhaus (Atlanta 2/8/89)
Mongoloid - Devo (UCLA 1/22/87) [can anyone confirm this?]
Night Moves - Bob Seagar (a few times, 1997, 2001, 2002)
Shout at the Devil - Motely Crue
Sparks - The Who (several shows in 2002)
Sweet Home Alabama - Lynyrd Skynyrd (several shows)
Symphony No. 5 - Beethoven (CSN 5/2/87)
Tahitian Moon - Porno For Pyros (Phoenix, AZ 11/9/01)
Tangerine - Led Zeppelin (Las Vegas 11/24/97)
The Bed - Lou Reed (Auburn Hills, MI 10/20/01)
Voodoo Child (Slight Return) - Jimi Hendrix (Seattle 4/17/89)
Walk This Way - Aerosmith ('87)
When The Levee Breaks - Led Zeppelin ("Live '86" cd)
Wild Thing - Jimi Hendrix (Cabo San Lucas, Mexico 8/31/02)
Wipe Out - Surfaris (3/29/87)

Non-cover covers (full length)
Happy Birthday Jubilee - Perry Farrell (many times in 2001)
Hungry - Dave Navarro (many times in 2001)
Pets - Porno For Pyros [w/Peter DiStefano] (Hollywood 10/27/01)