Ixion Saga Dimensional Transfer
A Fall 2012 to Winter 2013 anime by Brain's Base based on the online game Ixion Saga. The anime was adapted into two manga series and a light novel series.
The series follows male protagonist Hokaze Kon, a hardcore video gamer who gets transported to another world after accepting a request from a female character in a video game. Upon arriving in the other world he inadvertently saves princess Ecarlate Juptris Saint Piria and ends up accompanying her and her guards while she is trying to reach a neighboring country to marry its Prince and bring peace between their two countries. He helps to protect her as she is being hunted down by a militant faction of her own country trying to capture her and prevent this.
This tag implicates ixion_saga (learn more).