IIRC, the most in a week for me was 18.
Worst I ever had, though, was 3x round trips BUF-XXX-LAX in an 7 day timeframe.
Sunday ~ Early AM flight BUF-ATL-LAX then an overnight Renaissance LAX. Was relaxed pretty well and was looking forward to signing the new contract. Made the upgrade on both segments.
Monday~ Early AM meeting with new client and sign the contract. Meeting ends, go to LAX and catch last flight of the day LAX-CVG-BUF, overnight back in my own bed. Made the upgrade on LAX-CVG but no upgrade CVG-BUF as we had a Barbie Jet.
Tuesday~ Early AM and I'm in my office. Around noon a prospect that I've been calling on finally calls me back and thinks I'm still in LA as I had been leaving messages on his voice mail asking for the meeting since I was in town anyway. Anyway, he wants a lunch meeting tomorrow, so I go home, pack and catch last flight BUF-ATL-LAX and I overnight at Renaissance LAX. Made the BUF-ATL upgrade but missed the LAX one and had a crappy middle seat and I was starting to feel the effects of that much travel on my body.
Wednesday~lunch with the prospective client. Meeting goes well but long and there's no way I'm getting back tonight, so I overnight again at the Renaissance LAX.
Thursday ~ take the first flight of the day, LAX-ATL-BUF. Land and go to the office, was told that the client that I just signed the contract on wanted to go over a bunch of things for the setup and wanted me to meet all their team and I needed to go back to LA. Went straight back to the airport and ended up getting a BUF-CVG-LAX. Made both the upgrades early in the day and caught the BUF-CVG segment but missed the CVG-LAX segment. Overnight back at the Renaissance.
Friday ~ long ... meeting with the new client that I signed on Monday and I spent most of the day at their office. Decided to red-eye the flight back home and flew a LAX-CVG-BUF. Made the upgrades but couldn't sleep for the life of me (which isn't normal as I can sleep anywhere normally). Landed at CVG, switched terminals as I was on a CRJ-200, and proceeded to sit down and fall asleep. I had a pretty long layover, which royally sucked (like 3 hours or so), but it gave me some time to sleep. Luckily I woke up in time for the flight (my neck was another story as I kinked it pretty badly).
So, when people wonder why I don't do red-eye's anymore, that's why - I felt so crappy after all that flying and time changes that I vowed never to fly a red eye anymore.
I didn't keep up with my vow, but have only flown 3 red-eyes since that incident. 1 was to not miss my son's birthday party. 1 was because my wife went into labor early (they stopped it at the hospital but of course I panicked). 1 was for a client dinner in LAS where I had a function with the family that next day that I had to be at.