This varies greatly, but with some insurance you can only get medical coverage for yourself and your passenger (as well as underinsured/uninsured coverage) if you also get full coverage.
I sometimes tote a passenger on the Vee, so I keep full coverage for that reason, even though my bike isn't worth all that much anymore. The costs aren't all that high, especially if you carry a higher deductible.
And I hope it goes without saying that you should carry far more than the legal minimum liability coverage.
2002 Suzuki DL1000 V-Strom, Dark Metallic Space Blue
1983 Suzuki GS850G, Cosmic Blue
2005 KLR685, Aztec Red - Turd II.2, the ReReTurdening