I wouldn't jump to conclusions. Turns out it was a play format cause Bugs Bunny says this before the end..
Bugs:What did you expect from a opera? A happy ending?
There was one about a mutt falling in love with a sleek metal dog statue ("Ding Dog Daddy"). He had no idea that 'Daisy' wasn't real, and was completely gaga over her. At the cartoon's climax, however, her owners sell her to be melted down for scrap metal and reforged. The mutt takes off to save her, but ultimately fails and ends up left with the bomb her metal was used in. Completely wrecked, he cries "Daisy, what did they do to ya?" and gives her one last kiss — causing the bomb to explode. This being a Looney Tune, he survives and is even happily bouncing around at the end, thinking "She's still got it!".
Sylvester's breakdown in Birds Anonymous. Mel Blanc even said it was his favorite cartoon to voice for, especially when it came to Sylvester.
Sylvester: (sobbing) I can't stand it! I gotta have a bird! I'm weak! I'm weak, but I don't care! I can't help it! After all, I am a pussycat!
He has a similar breakdown in “The Last Hungry Cat.” In fact, several of the later Tweety and Sylvester shorts were less about Sylvester trying to catch the bird and more about him suffering internally from the guilt and shame of his “addiction.”
This line from the "Back In Action" movie, where we hear how Daffy feels about being in Bugs' shadow.
Daffy: What am I talkin' to you for? All you gotta do is munch on a carrot and people love ya.
When Mel Blanc died, what did they write on his tombstone? "That's all, Folks".
Also, the famous "Speechless" picture, with Bugs and the gang standing by a microphone with nobody beside it.
There's also the Friz Freleng version with Bugs and friends standing around an empty artist's desk, and another one with Yosemite Sam sadly riding away on his horse.
From "Broom-stick Bunny"
Witch Hazel: (crying) You remind me of Paul.
Witch Hazel: My pet tarantula.
A subtle one, but the short Moby Duck has Speedy spend the whole short trying to play nice with an exceptionally nasty Daffy when they are stranded on a desert island. When the latter refuses to share his new found supplies of canned food, Speedy plays keep away with a can opener until he negotiates. Daffy stubbornly refuses and goes through all sorts of hell to open the food himself, to the point Speedy just feels too sorry for him and gives it to him anyway, to which Daffy snatches the can opener and tells him to hit the road. Laser-Guided Karma comes through in the end, but that brief dejected look on Speedy reminds why he so rarely loses.
"Porky's Romance" has the title character coldly rejected by a mean spirited Petunia Pig. He slinks away in tears before contemplating suicide (and failing).
The final minute of "Zoom and Bored" took the coyote abuse too far. It gets so bad that he's actually sobbing by the end, to the point where the Road Runner doesn't even find it funny.
The part in “The Old Gray Hare” where Bugs pretends to die. Him saying farewell to a sobbing Elmer while digging a grave can hit a little hard, knowing that both their voice actors and all the original artists who brought the characters to life are now gone.
While a much more tongue in cheek case, there's something surprisingly pitiable about Elmer's crying fits (particularly his remorseful ones where he thinks he's finally killed Bugs). Friz Freleng stated this to be among the aspects of Elmer's character that he thought made him too sympathetic.
The first half of "Daffy's Rhapsody" (Before the song speeds up) is quite sorrowful, with Daffy explaining that hunters just won't give up in their attempts to hunt Daffy. (It's slightly dumbed down in the 2012 theatrical cartoon due to the constant slapstick, but still quite effective.)