I know far more game OSTs than anime, so maybe I can help there...I'd suggest stuff from the better known Legend of Zelda games - Ocarina of Time, right off the bat I can tell you Song of Storms
is an easily recognizable one, as is Zelda's Lullaby
or even the overworld theme
. Same goes with the Super Mario World
or even Tetris
As for lesser known ones, The Sun Rises
from Okami is great; as is any of the Chocobo Themes
from Final Fantasy (depending on which one you play can vary the difficulty of guessing). There's lots of things from Kingdom Hearts too, like the orchestral version of Hikari
or Dearly Beloved
As for anime...I do remember InuYasha having a beautiful soundtrack, as did Puella Magi Madoka Magica.
I happen to have the sheets for a lot of these too if you need them. They're fun songs to play fully, haha, but good luck with the panel.