More times than I care to admit.
-Lucario seeing Aaron's final words/dying
-Jirachi saying goodbye to Max
-Bulbasaur's near-death w/flashback sequence in his farewell episode
-The original trio's final battle/goodbyes in GCYL left me a puddle.
-Jessie and James getting destryoed defending Weezing and Arbok from the Poacher.
-James bidding Chimecho adieu
-'Snow Way Out' when his Pokemon agree to freeze to death with him
Oh and, of course, Bye Bye Butterfree.