So far, all I got are:

Creep - Radiohead

How Soon Is Now? - Love Spit Love

Buddy Holly - Weezer

Criminal - Fiona Apple

Eleanor Rigby - The Beatles

Fix You - Coldplay

Waiting - Green Day

Can't Take That Away - Mariah Carey

My Funny Valentine - Chet Baker

S'Wonderful - Diana Krall

When I Fall In Love - Doris Day

Oh So Quiet - Bjork

Here, There and Everywhere - The Beatles

Something - The Beatles

Isn't It Romantic - Ella Fitzgerald

What a Difference a Day Makes - Tony Bennett

Haven't Met You Yet - Micheal Buble

Rod Stewart. "Blue Moon"

Cat Stevens. " Hard Headed Woman"

Warning a few of these performers and songs are obscure.
1. Jackie Don't Go: Survivor
2. Broken Promises: Survivor
3. Its The Singer Not The Song: Survivor
4. Nothing To Lose: Gary Moore
5 No Easy Way Out: Robert Tepper
6 Said And Done: Message
7 Let Me In: Nick Gilder
8 Into The Night: Dakota
9 Call Your Name: Nightwing
10 Waiting 4 Love: Icebreaker
11 After The Hurt Is Gone: Strangeways
12 Face To Face: Strangeways
13 Its Not Over Til Its Over: Starship
14 Let Me Go: Y&T
15 The Last Time: Mark Free
16 I Still Believe: Tim Capello
17 Hearts On The Loose: Intruder
18 Love Doesnt Live Here Anymore: Michael Sembello
19 Through The Fire: Larry Greene
20 Never Surrender: Lion(God I love this song!

It's alright, so is most of my music collection.

The beauty of obscure music is that more than likely it wont be covered by a bad artist.
And while Im here I will mention more songs

Flight of Icarus: Iron Maiden
Only The Children: Toto

Bird on a Wire by Leonard Cohen
Pretty much anything by Joni Mitchell

Heart of gold - Neil Young
Lateralus - Tool
Be quiet and drive - Deftones
Self portrait in three colors - Charles Mingus
The amazing sounds of orgy - Radiohead
Warlock - Skinny puppy
Smokestack Lightnin' - Howlin' Wolf
Mezzanine - Massive Attack ( the whole album)
Vordohosbn - Aphex Twin
Policy of Truth - Depeche Mode
Boots of Spanish Leather - Bob Dylan
Lucky Man - the Verve