I work remote. Live in Virginia, work with a team in Pennsylvania, corporate headquarters in New York. How do I answer "Did you make money in any other states?"

Answer no, unless you spent any work time, even one day, in those other states or your employer withheld state tax for either of those states. 

I did have more than one business trip to Pennsylvania. 

   VA & PA are reciprocal states.  

 

In the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file a PA return.

 

For others reading this:

Q. Do you have to pay tax, to other states,  when you occasionally work in those (non reciprocal) states?

A. Yes, but "nobody" does. See http://money.cnn.com/2013/06/28/pf/taxes/business-traveler-tax-threat/  

If you live in a state without an income tax (e.g. FL or TX), it’s more likely you should file in the work states. You can't use the "it all comes out even" rationale for not filing.