My favorite characters are Desmond, Sayid, Locke, Hurley, Charlie (*sniff* I miss him!), Sun and Sawyer. I've never been much of a Jack fan. I think he is integral to the show and wouldn't want him to leave, but there is something about his character's arrogance and intolerance that just always rubbed me the wrong way.
Desmond talking to Penny on the phone in the Constant
Desmond and Penny meeting again on the boat
Desmond having 'flashes'
In fact - all Desmond scenes
Sayid at almost every time except when he was with Shannon. That was just.....wrong.
Locke realizing he royally scr***d up by destroying the computer.
Sun finding out Jin is the daddy
Sun confronting her dad
Sawyer conning the guns from the gang
Hurley being found out (in the flashback) by the reporters
Hurley in the mental hospital (all of those scenes are great)
Hurley saving the day with the van
Charlie's death. Sad, but awesomely acted
There's probably more. I love the show and rewatch the episodes when I can. I'm always finding new things to love (and discovering new clues).