I barely touch assembly in my day to day work, but I do understand on a fairly deep level how a computer works, which I feel is extremely important and very frequently influences how I write high-level code.

Certainly one can bang out code their entire career without ever having a clue how machine code works, but I really wouldn't advise it. At worst it leads to total ignorance, and at best you accumulate a disconnected set of "best practices" as inscrutable lore handed down from on high.