I've only ever had one I'd consider somewhat rare/unusual and that was a 1984 Honda VF1000F Interceptor.
It was my intro to sporty bikes back about 10 years ago. It was purchased from another member/friend here and I absolutely loved it. My oldest son had just gotten his motorcycle endorsement the year prior and had some miles in on a CX500 when he asked permission to ride it. My only requirement for him was full gear and keep it under 5000 rpm where the power band kicked in. He toddled off down the sidestreet and was gone for about an hour. When he came back, his eyes were like saucers and I fell over laughing, knowing full well he opened it up a bit. That thing had a wicked switchover when it hit.