It's funny that even in my limited experience, I've thrown a leg over a few of these. Yamaha XS650, KE100, Vespa, Yamaha Seca-UJM-thing, Airhead. I just bought the BMW 2 weeks ago after not having a bike since my teens because I wanted an excuse to sit in the garage and drink beer all weekend.
I think the best way to break this down is by categories. I know my answers aren't everybody's answers, but I like the category thing so Imma roll with it.
Something small, nimble, and friendly: Honda Cub or Vespa
Something small, nimble, with a Napoleon Complex: Yamaha RD350
Something terrifying: Kawasaki H1 or H2
Something huge and cruiser-ey: 1965 Electra-Glide (last year for the Panhead)
Something from Milwaukee: Harley XR1200
Something built to get filthy: Yamaha YZ250 - an old crummy one, with bumblebee paint
Something amazingly sorted and sensible: Honda VFR750
Something that eggs you on to do silly/stupid things: early KTM Duke
Something tempermental, absurd, and Italian: S4R Monster or 900SS
Something UJM: Kawasaki Z1
Something to get on and just go: BMW airhead
Something British: Yamaha XS650