Do condo associations have to file federal taxes?

Yes.  A condo association has to file federal taxes.

Do condo associations have to file state taxes?

Maybe.  This depends on the individual state.  

Why would a condo association file an 1120 instead of an 1120-H?

The simple answer is that the Form 1120 tax rate is lower than the Form 1120-H tax rate.  And utilizing Form 1120 can reduce the tax liability in situations where the association has higher amounts of non-exempt function income.  However, Form 1120 creates more complex calculating scenarios making them more costly.  Further, the audit risk is considered to be higher when filing Form 1120 instead of Form 1120-H.

What is exempt function income?

The broad answer is that exempt function income includes regular and special assessments made by owners to maintain association property. Non-exempt income, for most condo associations, is interest income from the association's savings and checking accounts.