There's a Harley IIRC which is LAMS approved. Someone I used to know owned one and loved it for the LAMS test. 400cc IIRC.
Got family with a Triumph Speed Triple... awesome bike.
Friend used to own a turbo Hayabusa and sold it because "I need my license for work, and in the 6 months I've owned this weapon, my license has copped a flogging". Downgraded to a GSX-R 600/700 (from memory).
I'd love a bike, but I honestly do not trust myself on them. Besides I like to really chill out whilst driving and crank the metal tunes, thus need some sub thumping action. Can't get that on a bike!