Some character deaths or near-deaths can be pretty intense; however they are never permanent, as the show is set in a video game.
A very heavily political-themed show, Log Horizon often exhibits betrayal and corruption as main themes. Also, people of grievously reminisce on the old world they once knew, and state that they miss their family and friends.
This show is not necessarily inappropriate for children, but most people under 12 or 13 wouldn't really understand a lot of the subject matter.
suggested rating PG-13 for some violence and brief language.