While technically not motorcycles, they do have two wheels, motors, and are driven on streets

Velosolex has been building motorized bicycles for a looong time. Here's a brief video clip of a bunch of Dutch people riding 2600 miles along Route 66 on them.

I think I actually saw something like this not too long ago riding around College Park.

I'd not looked at these for a long time, but they've become more popular since I last checked.

Cheap Chinese 2 stroke conversion kits are available to convert most bicycles into mopeds for around $150. Amazingly, many of these are equiped with catalyst exhaust systems now, even at that price.

I always thought that a *real* iron butt test might be a 300 mile day on a moped