I love the concept of catharsis- it's one of my favorite ideas to teach, although students get fouled up by thinking the character has to go through the purging of excess emotions instead of the audience.
It's a handy-dandy feature of tragedies: the playwright sees the audience laboring under excess emotions and gives them a chance to get rid of them.
I don't think catharsis works as well when the purging is directly connected to the event causing the excess emotions.
It feels good to vent, but I've never found that the feelings are gone after a good venting. They always build up again. I need to ride out the emotions, but I also need to work on the emotions. Haven't you ever seen a friend, after purging to you, go to the next person, tell the same exact story, and put themselves into the same tower of rage or despair?
In that situation, catharsis (and I don't even think it's a real catharsis) doesn't work unless you or I or they reconcile, accommodate, or assimilate the experience. Otherwise it's a rut to be retread, and kind of tiresome for all involved.
The best catharsis comes from imitations (plays, songs, movies, or books), not real life. Either I'm unaware of my excess emotions or I have a lump in my chest and throat that will not dissolve. Then comes the movie or the song, and I'm weeping- letting go and restoring balance.
My favorite catharsis came from reading SECOND NATURE. My dad had died and my grief wasn't on a surface level anymore, but when I read the description of a character's death, the tears started and didn't stop until the front of my shirt was sopping. Which is one of many reasons I love, and will always love, Alice Hoffman.
Balance was ever so important to the ancient Greeks, and excess emotions were unseemly. In fact, one of the major complaints from the chorus chucked at Medea's head was that her feelings were over the top (this was before the killing of the kids entered the playscape). I love the concept of equilibrium, and one of the purposes of simplifying my life is always an effort to get me in balance. But I'm usually a gnarl of internal excess, consciously and unconsciously, and thank the gods that catharsis is available.
Cathartics off the top of my head? The song "I Will Remember You", THE ROAD (only once because that shit stays with you), the ending of THE FELLOWSHIP OF THE RING (Sam Gamgee, I heart you), The end of BUFFY- second season, and the part in THE LION KING when Mustafa talks to Simba about the stars.