Jazz in Metal?

Are there any metal songs/bands that have jazz or jazz roots?

yes - in several veins.

In traditional speed/thrash/pop - the jazz influence is hard to see. Example: Look at some Anthrax (among the living era), and compare it to Charles Mingus, you may be pleasantly surprised (some Ancient Chinese secret, Scott ?)

Musical phrasing of metal stems from Jazz - and it echos clearly in Mustane's bridges (Think Bitches Brew), Iron Maiden's duo-phonic phrasing, Phil's meandering second verses (Sacred Reich). Yes , Jazz is alive and well in metal.

In grindcore - compare the free-syllable phrasing of Billy Holiday to the singing on Harmony Corruption - how 9 syllables will fit into 8 bars so naturally (I know you didn't like that comparison, then... or now, Barney)

In Death metal ..... hmmmm
<thinking>
ok - take the changes that Dimmu Borgir uses in their songs, and then remember Charlie "Bird" Parker or Frank Zappa, and their unexpected time changes.
Also - think of Gallespie's music, and key change mid song. Look how Mayhem or Tiamant music has benefitted from such.

Metal has deep and clear roots in Jazz.

Yeah! All the bands that are classic rock or will become have elements that can be traced back to blues and jazz. That's what spawned rock n roll in the first place.

If you're looking for specific examples where metal and jazz co-exist, check Faith No More - specifically their 1995 album titled "King For A Day, Fool For A Lifetime".

Types of metal(mostly apparent in progressive or death) have jazz-like drumming and odd time signatures.

But if you're thinking what I'm thinking, pick up some Atheist.

If you're looking for DIRECT jazz sounds in metal that you can hear, and you don't have to "trace back", check out Candiria's first album 300 percent density,

or even better Into The Moat's album "Design".

You can hear it directly.
It's there.

I'll answer your question this way:When Charlie Parker invented bebop in the 1940's, he changed the way all pop,,jazz, and classical musicians played. So either consciously or unconsciosly when you hear an awesome lick on any instrument(drums included),it stems from bebop,the first music to be called "modern jazz."

Dark Hall.

I will second the suggestion to check out Candiria. They are amazing live, and their drummer is a powerhouse who is also a huge jazz and fusion fan. For a more extreme free jazz vibe, check out The Dillinger Escape Plan or John Zorn's Naked City.