I jazz, we typically see 7th chords, whether they are Maj7th, Min7th, Half-diminished 7th (dominant 7th), or fully diminished 7th.
The best way to learn these, in my opinion- is to utilize them in the context of one of the several jazz standards. Start simple, and pick up a Real/Fake book and work on something like All Blues by Miles Davis. Listen to the song, learn the melody, and learn the chords. Once you've got the song down, try learning it a completely different way- playing the melody in a different place, playing the chords in a different place (different inversion), I find this very useful and important and you will learn a lot from doing that.
The other chords you will see are 9 chords and 6 chords. So a Dmin9 or a EMaj6 for example. Same deal, utilize those in the context of one of the many standards. You'll find a whole assortment of chords in there.
Then you start to add things on top of chords, like #11's, and 13's, and #5's and a few more. So a chord might read Dmin7(b5), or A7(b9). But just like I said before- you'll find these in the standards left and right, so get a book to see where they are- learn the songs, and learn them in as many different ways as you can.
My email is [email]aweibe@gborocollege.edu[/email] , feel free to email me if you have any questions.