I actually started this discussion on the LANDMASTER Meme, but now I think this should focus on Brawl-Memes in general.
I remember when Brawl was coming out a lot of fans hung around the GameFAQs forums. I remember a lot of people speculating what each character's Final Smash would be, and hoped that no clone characters, if they were put in the game, had the same Final Smash. When we learned about Fox's Final Smash, the Landmaster that first appeared in Star Fox 64, we were excited. However, when we learned Falco's Final Smash was also a Landmaster, we began to worry. When we finally found out Wolf was in the game and had the same Final Smash, people just got outrageous. Almost every other topic would have some form of LANDMASTER! in it. Also, I remember someone photoshopped a non-Star Fox character in a picture with two landmasters, joking that every character had landmasters. I think Landmaster became a definition on Urban Dictionary that meant something that's overused or unoriginal
Other memes include the short lived Phenis Punch, a typo someone made on GameFAQs when trying to talk about Captain Falcon's signiture move, the Falcon Punch, and confusing it for a Pheonix. Two other memes were YOU MUST RECOVER! and laughs, the first referring to one of the many strange, quotable posts of creator Masahiro Sakurai on smashbros.com and the other part of an Iwata Asks interview between Nintendo's president and Sakurai, where the line "Sakurai: laughs" showed up multiple times.
One last meme is kind of a stretch, but I remember a fake Smash Dojo being updated at the same time as the actual Smash Dojo. I can't remember the name but from what I remember it would post rediculous Brawl characters such as Bill Cosby. Can anyone add anything else?