soulgrindr: Airwolf on the zx-spectrum.
I don't know if anyone ever completed it on the original machine, or just on emulators where they had the ability to slow the game down.
I must have played it dozens of times and never made it past the first force-field. Never even got as far as an enemy!
Turned out it was only about 4 screens long... but they made it so hard that i think very few people ever found that out.
Airwolf wasn't that bad. I managed to get to the end and back a few times as a kid and I'm sure some of my mates could do the same. Having said that, to beat the game you had to do it about 5 times in a row which I certainly never got anywhere near.
If you want a really hard speccy game how about the Jet Set Willy clone Technician Ted. There were a huge number of rooms and you had to complete the 21 tasks in a given order (except you weren't told what the order was). All the rooms kept changing as you played, loads of the jumps had to not only be pixel perfect but also timed perfectly and to top it off you had a time limit so harsh that even if you played through the entire game never making a mistake during 50 minutes of gameplay you would barely scrape there in time. Its a game so hard you would have to dedicate years to beating it without cheating.