This article is from the Beginner Motorcycle Info FAQ, by firstname.lastname@example.org (Ravi Narayan) with numerous contributions by others.
Most car companies don't cover bikes so you will need separate
insurance. Some car companies only cover smaller bikes.
Cycle insurance is first of all based on the size of the bike, then
record, age and other factors. A 25 year old with a GS450 can pay
less than $100 a year, an 18 year old with a ZX-750 (ie. a ninja)
can pay up to $1000 per year. Cycle mags often advertise companies
that cover cyclists, you can also get it through dealers, most have
an association with one or another company.
In an accident with a car, you and your passenger will probably (I
know all accidents are different!) incur the greatest medical bills
while the car will incur the greatest property damage. The bike
will probably be in worse shape than the car, but unless you have
a fancy new bike the car will probably cost a lot more so
$$$damages will be higher for the car than the bike. Think about
this when deciding what coverage to get.