Jazz Songwriting Inspiration

First pick the Key/Mode that you want to compose in. Then select the number of chords that you want in the progression. Next, select how you want the progression to end (any chord, on the tonic, sub-dominant, etc.)
Finally, click generate, and a progression will render.

The chords are quasi-random, but based on a proprietary ruleset of chords that sound good together. The rendered progression should sound decent, but if you don't like how it sounds, just hit the generate button again. It's that easy.

Also, you can play the progression to hear what it sounds like. There are 3 audio options (piano, electric piano, guitar) so that you can get a feel for the progression.

Finally, you can print the progression, making it ideal for a teaching situation, or just convenient to put on your sheet music stand.

BONUS: Save to Music XML Format and import into Logic Pro X (Sibelius also supports Music XML.) Just save your chords to XML, and select Import Music XML from the Logic Pro X menu. You'll go from no music idea to a song outline in a few minutes. Additionally, it'll take the root note and create a separate bass track as well as the 5th note and make that a lead or comp track. Just assign whatever patches/instrument to each track that you like. It couldn't be easier. (I'm actually a bit ashamed to use it because it makes it so effortless and fast to compose. It feels like cheating.)

The best way to use it is just to select 32 chords and ANY ending, and just jam to the progression. The odds are low that all 32 chords are going to give you a great song, but there should be a sub-progression of 3 to 4 chords that will spark some creativity. Hopefully they'll generate new ideas based on chords that you typically wouldn't pick.

There are also some common pre-canned progression that could prove useful, for example the 12 bar blues, and the common jazz progression of 2-5-1, as well as some other common standards.

If you are trying to write more of a radio friendly pop style, or something like tropical house, then selecting a pattern ending with IV-I or V-I, and with a length of 4 or 8 chords, should yield the best results.