I've seen in excess of 800mph, the pilot telling us we had a tailwind slightly exceeding 200mph. Most aircraft stats I've seen have a cruising speed of 575'ish, which is relative to the airflow, so upper 700's-800 isn't our of the question.

Going the other way, you're chugging away at about 375. That makes for a long flight. In reality, I suspect the flight would be routed around the jetstream, where possible.

From the site above, it looks like 734 knots, or 845mph, is the fastest captured for a commercial jet - an A340. That looks like it had a 275mph tailwind. Wow. (Of course, there's the Concorde at 1386mph...)