Atlantic flew the Electra with just two pilots (no F/E). I think they were the only Electra operator to do this.
And Air Canada flew the mighty DC-8 with two pilots, no FE as I recall. There were extended seat rails in the floor so the FO could slide back to the panel and play with the bells and whistles (but don't touch those white knobs on the fuel panel
).
The A300B4-600 did away with the Flight Engineer, (bloody computers).
I think some companies, possibly Air France for one, initially operated the A310/A306 with an FE.
I remember riding on an Eastern A300B4 jumpseat years ago, the FE said she was deadheading between preflights.
The L1011 FE job also looked pretty cushy to me back in the day but they were long gone before I got to a couple of carriers that had them.
All I remember about being an FE is 'Check Essential!' and 'Drop-rise, drop-rise'...
On the US Military side these come to mind:
I'm thinking some of these no longer have a flight engineer. For example, from the Air Force KC-135 information page:
Three: pilot, co-pilot and boom operator. Some KC-135 missions require the addition of a navigator.
KC-135 Stratotanker > U.S. Air Force > Fact Sheet Display