I like musicians who "look the part." This has a lot of implications in country/Americana music but for right now I'm going to limit it to areas outside those realms.
The bands I love seeing are those that epitomize some kind of romantic ideal of the music. Here are some cases in point:
Distraught tortured singer-songwriters who look to the bottle for comfort:
Ryan Adams
Conor Oberst
Ridiculous bands who let their sense of fun SHINE:
Flaming Lips

Sufjan Stevens

Of Montreal

(maybe there needs to be a subsection dedicated to guys who wear wings on stage)
Hipsters: Dean and Britta

And then there's Jack White, the king of image:



