I was sent out of state for work training for a week. Do I have to file taxes in the state I traveled to?

No.

Since you were not working  -you were learning - in the state and did not earn income from that state while there, you have nothing to report.

I assume you were being paid, your regular salary,  by your employer, while you were at this out of state training.

Q.  I was sent out of state for work training for a week. Do I have to file taxes in the state I traveled to and effectively worked in for a week?

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.