It's been mentioned already, and for obvious reasons but Gerrard against West Ham in the FA Cup final is my favourite ever goal for a number of reasons. The timing of the goal, as well as the imoprtance of it being in a cup final, added to the actual quality of the goal make it undoubtedly one of the greatest in LFC history, hence it being mentioned so many times already in this thread, but the memories i've got attached to it make it even more special.
I remember going to the pub with my dad to watch the match, and i'd been stood with him throughout the match. When Gerrard scored the equaliser I turned round expecting to see my dad but he wasn't there, he must've gone the toilet thinking the game was over but before i'd had a chance to even look around properly I was jumped on by a mate of mine who I didn't even know was in the pub watching the game until that point. I remember the euphoric feeling of celebrating that goal like it was yesterday, and the memories are much clearer than Istanbul because I was much more sober for the FA Cup final than I was for that.
The mate that i ended up celebrating the goal with tragically passed away a few months later when he was only 18, and I hadn't spoken to him since the cup final day, so whenever I see Gerrard's goal, as well as bringing back memories of a great FA Cup win, it brings back the memory of my mate, which is the last memory I have of him, and which is fittingly of him jumping up and down celebrating with a huge smile on his face.
http://www.youtube.com/watch?v=IXUWFIVNqpYAnother of my favourite ever LFC goals also links in with this story, as on the day of the lads funeral a load of people went back to his local after the service. Liverpool were playing Newcastle that night and it was being shown in the pub that we were all in, and I remember it well because it was the 1st and only ever time i've felt like a Liverpool match meant nothing to me, I was even one of the few who still felt interested in watching us under Hodgson, but this night I was completely disinterested and didn't even bother to watch most of the match, but on one of the few occasions I did look up at the screen it was just in time to see Xabi Alonso float the ball over Steve Harper's head from within his own half.
http://www.youtube.com/watch?v=S3oc9rNQLuU&feature=relatedUnlike the 1st goal which is a favourite of mine for the memories of euphoric celebrations, this goal is important to me because it taught me valuable lesson, something which goes against the words of the great Bill Shankly, but it taught me that there really are more important things in life than football.