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
K-On! or Aria
I can basically just throw on any random episode of either series to just chill out / feel better
likewise with Ghibli stuff obviously, which I end up rewatching movies from almost every year
in terms of plot driven stuff probably Eva, Planetes, Stand Alone Complex, Legend of Galactic Heroes, and 3-gatsu