My favorite part of portraiture-- I think-- is finding a fantastic pose or composition that makes the final portrait insightful and un-cheesy. I need to remember, when doing quick portrait sketches, to take a little time before I start to consider pose and composition. These are some really interesting ways of portraying someone besides the "sit for a mugshot."
Marcel Duchamp. Nude Descending A Staircase. [This may not be a portrait but I used it for the idea of a portrait in motion. Duchamp actually painted the very similar Sad Young Man in a Train, which he identified as a self-portrait.]
Marcel Duchamp. Self Portrait.
Edgar Degas. Portrait of Duranty.
Degas. Portrait of Diego Martelli
Norman Rockwell, The Problem We All Live With.