You could easily compile a list of the top twenty famous goals both scored and conceded by us. But sometimes the most important goals are the ones that happen in matches that don't mean a lot in themselves but have tremendous consequences for the outcomes at the nd of the season.
Three have already been mentioned this thread
Tommy Booth's goal against Peterborough in 81 cup run, although you could say the same about Paul Power' equaliser against Everton
Kolarov's goal against Sunderland in 2012 which gained us a point in game we should have probably lost.
David Silva's against Hull in 2014 when he decided that he was going to everything he could to make sure we won that game after Vinnie got sent off. Though special mentions need to go to Javi Garcia and Martin Demechelis for their Dias and Stones like performances.
The others that spring to mind are;
Jim Tolmie and Kenny Clements against Sheffield United in April 1985, we desperately needed to win to keep in the promotion race but were bloody awful all game. But in the last minutes we managed to score two almost identical goals from the right hand side of the penalty area to give us the win.
Samir Nasri's goal against Sunderland in April 2014 which trickled over the line after Manone only half stopped it to save a point in another game where we weren't at our best.
Finally Sterling's goal against Southampton in 2017 which kept the winning streak going in a game that was probably destined to be a draw. One of those cliche games where Champions find a way to win.