Mine is probably Hodge structure of motivic or representation theoritic objects. I know it's essential and extremely important and stuff. But I just can't see the beauty in it.
I need it all the times and its presence matters enormously. Sometimes I work with PEL Shimura varieties just to avoid having to deal with the Hodge questions. I couldn't escape it though this time as Hodge structure provides a controls the behavior of L-functions at infinite places.