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)