Traditional (Trad) Jazz also known as "Dixieland" or "New Orleans" Jazz

Bix Beiderbeck - Jazz Me Blues (1927) http://www.youtube.com/watch?v=O7be5YL3tiQ

Louis Armstrong - Basin Street Blues (1959) http://www.youtube.com/watch?v=6GuDExkBmnU

Nicolas Payton - Weather Bird (1995) http://www.youtube.com/watch?v=ZvtOQexQnsU

Swing (Swing / Big Band Era)

Harry James - You Made Me Love You (1941) http://www.youtube.com/watch?v=YTQVWtSvwUE

Clark Terry - Pennies From Heaven (1977) http://www.youtube.com/watch?v=_H3zJrZcycY

Bebop

Dizzie Gillespie - Hot House (1952) http://www.youtube.com/watch?v=Clp9AeBdgL0

Clifford Brown - Joy Spring (1955) http://www.youtube.com/watch?v=6tBJa8Ew6fQ

Modal

Miles Davis - So What (1953) http://www.youtube.com/watch?v=V1hT2u1jwcs

Freddie Hubbard - Maiden Voyage (1965) http://www.youtube.com/watch?v=hwmRQ0PBtXU

Avant Garde / Modern Jazz

Dave Douglas - Charms Of The Night Sky (1997) http://www.youtube.com/watch?v=LBIevdmrCx0

Electric Jazz

Miles Davis - Tutu (1986) http://www.youtube.com/watch?v=6Xs2XelLAfA

Randy Brecker (1992) http://www.youtube.com/watch?v=UIGsSLCoIhM

Smooth Jazz

Chris Botti - Lisa (2001) http://www.youtube.com/watch?v=UTCsU0pzCFM

Chet Baker - She Was Too Good To Me (1974) http://www.youtube.com/watch?v=cevs8ZgUb2A

Big Band

Maynard Ferguson - Birdland http://www.youtube.com/watch?v=MQvRP50WWXg

Harry Connic Jr. Big Band (Roger Ingram - Lead Trumpet, Leroy Jones - Trumpet Solo)

http://www.youtube.com/watch?v=QwUu6JYl9EU

Click here for a link from the wiki page on Jazz Styles

I would also suggest watching the "Ken Burns Jazz" series... Hosted/Narrated by Wynton Marsalis, it takes you through the history of Jazz with many videos and musical clips.  (you might be able to find clips on youtube or get the DVD's from your local library)