We’ve already mentioned TMNT1 for the NES once already, but I think the water mine-defusing stage deserves special mention. The controls were none too great, and that time limit… ugh.
Final Fantasy XI had more than its fair share of frustrating moments, biggest of which is EXP loss upon death and ‘level down.’ I can never forget that noise… Also, leading a team of people to beat the Chains of Promathia missions right as they came out is one of my proudest memories, but also one of the most frustrating. The missions were not explained very well and they were HARD. My group of 6 was the 2nd NA team to get sea access.
Oh, I almost forgot. Aladdin, for the Genesis. The Cave of Wonders escape level. The horror.