I agree with Sharp11Thirteen. If you rule out the progressions chrisjh listed, you'd be left with little to use. Most of those progressions ( such as the I | IV, the i | IV, the I | IV | V, and the ii | V | I ) are simply Tools to use to sculpt your final musical piece.

Like what Sharp11Thirteen said, the reason they are overused is also Context. Charles Mingus and Thelonius Monk could write totally far out progessions, and then Tease a silly ii V I in somewhere, as a musical joke. Frank Zappa would have a large Verse-Chorus song, and tease an entire Blues chorus as the bridge, and then jump right back in where he left off. These guys used the common stuff specifically when it was appropiate. Yes, they are still common, but now they are something Special.

Also, plenty of guys have modified and changed common progressions to get a new sound out of them. Sonny Rollins took the very common Rhythm Changes and changed a couple chords with substitutions and made 'Oleo'. Charlie Parker took Rhythm Changes and put ii V's in the bridge, and called it 'Dexterity'.
John Coltrane uses only 3 different ii V I progessions in different orders and such, to create a pattern that became 'Giant Steps'. It's only 3 different ii V I's... -just Three!- and it is one of the most unique, even difficult, songs in jazz. Coltrane also took that pattern, slightly modified, to change Mile Davis' 'Tune Up' into 'Countdown'.
Also, little things make big differences. Thelonius Monk ('Blue Monk') put a #IVdim7 in the sixth measure of the blues. The Chromatics make a hip new sound that is unmistakable. And the boys from Steely Dan, who would take the blues, and alter it into this new being in tunes like Black Friday, Bodhisattva... and in a way, even Peg.
And the Tritone Substituion ( ii bII7 Imaj7 ) that Sharp11Thirteen meantioned is a great example of a common porgression, slightly modified to create something very new Sounding.

If you want New progressions unlike anything else... Check out these Jazz Standards (lead sheets available in the Real Book). Check out Herbie Hancock's 'Maiden Voyage' and 'Butterfly'.... no ii V I's or other boring progressions there... Or Coltrane's 'Crescent' and 'Lonnie's Lament'. Both very unique progressions. 'Fables of Faubus' and 'Jump Monk' by Charles Mingus are long heads that aren't simple changes or patterns. Freddie Hubbard's 'Red Clay' is an awesome display of jamming out on a unique, new form. 'Peaches en Regalia', Frank Zappa's epic tune: long and building. And Miles Davis/ Wayne Shorter's 'Nefertiti' is a beautiful and unique Ballad, unlike any hokey ii V I ballad heard before. Also, 'Naima' by Coltrane is a great ballad, too. 'Space Circus' by Chick Corea. 'Speak No Evil' by Wayne Shorter. 'You know, You know' and 'Awakening' by Mahavishnu Orchestra.
If you want to ditch ALL progressions flat out.... check out Free Jazz... John Coltrane's A LOVE SUPREME album, and Miles Davis' BITCHES BREW are milestone albums for the free jazz school.

In rock, there's Radiohead, Tool, Incubus, Primus, King Crimson... all taking things away from traditional music.
Check those out for more far out music...you wont be let down, man.