It depends on the company you work for. Generally you will be allowed free travel (space available) on your own company for youself, your spouse, your dependent children, and your parents. In some cases, depending on the company, an unmarried significant other (or other travel designee if you're not married), can replace a spouse.
Generally you will also receive either free or extremely reduced travel on any partner companies (IE if you work for Comair/Delta Connection, you get benefits on other Delta operators such as mainline, ASA, Skywest).
For non-affiliated airlines (such as NWA if you work for United), most airlines have non-rev agreements that allow for either fixed rate fares (such as $30 per segment) or sliding scale fares (zonal or ID90/ID85).
When I worked for Atlantic Coast Airlines, we had travel benefits on UAL and Delta, plus agreements for reduced travel on about 50 other carriers, including foreign operators.