No one has mentioned Spongebob? I see him mentioned on just about every thread in TZ in some way, but we've gone this far into an 'EFFEMINATE CARTOON CHARACTERS" thread and I haven't seen his name? Unbelievable!
Bugs Bunny wasn't so much effeminate at all, but he pulled off 'being a girl' quite well.
Heffer's brother from Rocko... the son of the wolf family. I forget his name, but I remember at least one or two occasions in which he was doing something 'girlish' and ragged on his unapproving father: "Judge, judge, judge!"
On that note, I'm reminded of Bobby Hill, who in every other episode of King of the Hill gets involved in something "girly" in the eyes of the average manly Texan, much to the dismay of Hank.
And another from a Fox mature cartoon, the alien from American Dad. I've only watched the show a couple times, so I can't be bothered to remember his name, but he was quite girly.