I actually read surprisingly little fic these days, and when I do it's mostly slash. So this is a bit old now, but this fic made me fall in love with a character and it made me fall in love with a ship. In fact, that is one of the reasons I love fanfic - that a fic can give you a whole new perspective for not just a character, but a relationship and the a show as a whole.
So my rec is gyzym's 'An Avalanche of Detour Signs'. It made me ship Molly/Lestrade like you wouldn't believe, and it really gave me an insight into how hard Sherlock's disappearance must have been for Molly, knowing the truth all along when even John didn't.