Re the "crossover" etc. comments, third stream, fusion, ECM style, etc. are considered subgenres of jazz (despite Gunther Schuller's and others objections re third stream--conventionally it's treated as a jazz subgenre).
Re Art Ensemble of Chicago, a lot of their stuff, especially their earlier stuff, was free improv under a jazz rubric. Arguably some free improv wouldn't fall under jazz, but that's arguable.
And on the other side, Copland's Music for the Theatre (which has a heavy jazz influence), Four Piano Blues, etc., Stravinsky's Ragtime, etc. are considered classical.
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