Praise be to Allah.
Motorcycles, like any other means of transportation, are permissible in principle, so long as there is nothing involved that would dictate disallowing them.
For more information, please see the answer to question no. 172612
With regard to the dangers involved, this is a relative matter that varies from one situation or individual to another. A motorcycle may be ridden by one who does not handle it well, or who uses it as a means of showing off, such as riding it up to high places or doing stunts in the streets, and other things that happen nowadays, the consequences of which may be serious. There is no doubt that it is haraam to do such things.
Or it may be ridden by one who handles it well, in which case it is like any other means of transportation.
And Allah knows best.
Reproduced from Islam QA