It's definitely a toss up for me. I think at this point I've seen The Melancholy of Haruhi Suzumiya more than any other series. It's pretty much my go to series whenever I'm down. It has it's issues, but I really like the characters
I've also watched both Boogiepop series and Bloom Into You many times as well
edit - adding D-Frag as well for feel good series I watch almost once a year
Used to watch the 1990 Moomin anime a fair bit as a child.
Otherwise it is probably watching Paranoia Agent, Black Lagoon and Samurai Champloo out of order on TV.