I have recently been reading Stephanie Dalley's translation of Mesopotamian myths. In Erra and Ishum, Erra claims to be, among many other things, to be the "campaign standard." This made me wonder whether any of the ancient Mesopotamian kingdoms/empires like Babylon or Assyria had military standards like Rome's famous eagle standard. A quick search did reveal that ancient Egyptians carried known standards into battle, but nothing in Mesopotamian armies.
Did they have notable or any known standards that were brought onto the battlefield like the Romans eventually did?
If it helps any, Dalley says in the text that it was probably written around the 8th century BC, and it ends with a note by a Neo-Assyrian king at the end.
Assyrians definitely utilized divinely-linked battle standards. The most thorough source I could find is Steven Winford Holloway's Aššur is King! Aššur is King!: Religion in the Exercise of Power in the Neo-Assyrian Empire, specifically Chapter 2 in the section on "The Symbol of Assur", starting on page 160. Most of that should be available on google books.
Apparently a comprehensive source on Assyrian battle-standards is K. Deller's Gotterstreitwagen und Gotterstandarten, but it's in German and I can't find it.
Anyways, it sounds like they carried them into battle on the backs of chariots (on the basis of iconographic depictions in palaces and on stele), flew them above cities as a sign of successful conquest, and they were either stored in the deity's temple when not in use or alternatively, were counterparts to the icons of the temple deities.
I recommend reading Holloway's chapter; it's not primarily about military standards but it's got a lot of interesting info about them and the general cultural context of Assyrian military/religious connections.