If you have some money saved up, you are essentially self insuring yourself up to a certain point $2000 to $5000 is common (or more).
No frills, high deductibles, this is the name of the HSA game.
In addition (to your premiums) you can bank extra money as explained above. It all comes down to this is catastropic coverage, and how much risk you are willing to take.
Source: http://www.goquoteme.com