There are so many but here are three great ones:
Rock:
Unchained Melody - Righteous Brothers
Sun King - The Beatles (or the Beach Boys?)
Smells Like Teen Spirit - Nirvana (when we all thought it was said and done)
Hard Rock:
One - Metallica (possible birth of Djent)
Surfing with the Alien - Joe
White Room - Cream (inspired many)
Motown, Soul, and R&B:
Where Did Our Love Go - The Supremes
Superstitious - Stevie Wonder (talent incarnate)
September - Earth, Wind, and Fire
Acoustic:
Hotel California - The Eagles (changed what I thought one song could do)
Better Place To Be - Harry Chapin (changed everything about what I thought music was about)
and for my most favorite unknown song, this:
http://www.youtube.com/watch?v=ickWCGc5qHw