The truth is that back taxes are dischargeable (able to be eliminated) in bankruptcy if they're "old enough". We'll take a look at what that means.
To be dischargeable, back taxes must satisfy all three of the following rules:
Three Year Rule
The tax return was due more than three years before filing bankruptcy.
Two Year Rule
The tax return for that tax year must have been filed more than two years before filing bankruptcy.
240 Day Rule
The income taxes were assessed (if they were assessed) by the IRS (or California FTB) more than 240 days prior to the bankruptcy filing.
In addition, there must have been no fraud involved.
This is the very short version. For a longer version, see this article.
If you think this applies to you, it's definitely a "don't try this at home" sort of deal. Definitely retain a bankruptcy attorney experienced in discharging back taxes.