I was traveling from Dfw-SFO (AA) and SFO- Taipei (Eva Air) I brought 2 suitcases and AA charged me $60. Has this ever happens to anyone? Their reasoning was that Eva Air is not part of One World.
Checked baggage rules depends on the purchased ticket and eventually to a frequent-flyer program status of the passenger.
Let's say for example that you purchased a single ticket from Dallas to Taipei economic class with a single checked baggage. Because you have the status X of the frequent-flyer program Y and the company that is serving your single ticket recognize the frequent-flyer program they give you an extra checked baggage for free valid for all the trip.
Another example: you bought two separate tickets, one from Dallas to San Francisco and another from San Francisco to Taipei (economy class and 1 checked baggage allowed). In this case only the flight from Dallas to San Francisco is served by a company that recognize your frequent-flyer status and give you the extra checked baggage only for that part of your trip.