Photoshops are worth quoting if they're funny.
Other pictures are good if they're informative or interesting (such as the picture that compares the character models of the original, Melee, and Brawl.)
Funny posts are absolutely worth quoting.
Accurate predictions are only good if they're really prescient predictions. Like, that guy who predicted the Dragoon levels of prescient.
Inaccurate predictions are only worthwhile if they're so wrong or so firmly stated to be true that it's funny. For instance, a quote in my first section has SantaC saying that people who say Sonic is in the game are deluding themselves. I thought that was so wrong, it was funny.
Reactions to a megaton...well, some of them can be amusing (the Stage Builder, Sonic, even Olimar), but we shouldn't go overboard.
Ban bets are only worth posting if they actually went somewhere.
Meltdowns are always fun to watch.
Sorry Jiggy, I'm a huge fan, but even I don't think that every one of your stats posts deserves to be quoted.
Still, notably good ones are definitely worthy. Incidentally, I think my section has the very first Jiggy stats post, though I may be mistaken.
Random philosophical stuff is awesome. Do want.
The only other category I can think of would be debates on random subjects, though I'm sure many of those can go under other headers.