Whenever my internet is out, my library will be there to save the day. (It includes books, animes, mangas, comics, novels, video-games. My prized collection which I gathered over the years)
For emergency anime I have the box sets (along with their movies) of Ghost in The Shell, Gundam Z, Evangelion, Steins;Gate, along with other classics. While I do own physical copies of many anime series, these are my go-to-watch series in emergencies.