Naruto's continuous attempts to force Sasuke to come back to the Leaf Village, even if he clearly doesn't want to, have been interpreted by fans as overly annoying, even because it's actually what the overall plot consist on.
The series' Uchiha clan as being masters of "the Art of Run," a ninja technique that looks suspiciously like running away from your opponents. The meme originated because the ambiguous villain Itachi Uchiha of the clan has on numerous occasions begun a battle and then left the scene after exchanging only a few blows with the series's heroes.
In addition, it has been common to mark members of the villain group Akatsuki for death once they take off their cloaks (which has been accurate for seven of them so far),
Recent chapters reveal that THE ORIGINAL Madara Uchiha is revived by Edo Tensei, raising questions on WHO IS THE GUY IN THE MASK?
More Explanation
ToMaTo is a nickname for this guy who could possibly be one of these characters: Tobi, Madara, ObiTo. As of this reveal it is very unlikely to be Madara.
Lately it's been something of a meme that anyone covering an eye has a Sharingan (or more rarely a Byakugan or Rinnegan) unless proven otherwise. This also comes with the revelation that "covering an eye" describes like 20% of the cast.
After Danzo's took his arm out, it seems it doesn't even need to be an eye, it's just anyone covering any part of their body.
Sharingarm.
With optional Shouldai
SHARING IS CARING.
SASORI, MY MAN!
Itachi also wants you to know that you lack hatred.
And Sai wants Naruto to know that he lacks penis.
And that even your dog is smarter than you.
And that he likes ugly bitches like you.
And also, don't put him in the same group as that gutless little homo (Sasuke).
Sasuke's rapefaces from the latest chapters achieved memetic status fairly quickly.
Itachi's Not So Stoic facial expression from chapter 386. >8D
"Yamato Wood◊", which was spawned from a rather oddly drawn panel of Yamato, often a subject to photoshopping onto various naked characters implying he just raped someone, with him saying "HELLO FRIENDS".
Uchihahaha!
Really, any Not So Stoic moment from the Uchiha is met with an "OH EXPLOITABLE!"
NINJA TANK (from fake spoilers saying that in Chapter 465, Madara and Zetsu turn up to Sasuke's rescue with a tank containing Itachi's Eyes. You can figure out why).
From the 13 ending of Shippuden, which put a catchy yet repetitive song featuring a character, up to and including the episode that ended with severe Mood Whiplash and that character being beaten rather soundly.
"It's true you were special but I am more special than you!"
Sasuke, you're special, alright.
Much of chapter 500 quickly became a meme shortly after it was released. For example:
"Fourth Hokage...Minato. Back away from the jinchuuriki or your son dies at the ripe old age of one minute."
Then there's the Running Gag among the fandom that the series itself should be called "Sasuke", in reference to the fact that it recently seems like Sasuke, not Naruto himself, is the main character.
Chapter 476: Naruto hyperventilating and fainting.
KakuzuExplanation
This stems from a moment on TV Tropes' Naruto thread in the forum, in which someone asked a spoiler-sensitive question, to which multiple people answered within seconds of each other: Kakuzu
Who exactly is going to be the final enemy of the series has been the source of heavy speculation and debate for a very long time, and thus the source of more than a few jokes.
Any time Might Guy and Rock Lee have a bonding moment, an unbreakable genjutsu involving a sunset and a crashing wave is created and the image is placed in your mind for as long as you live. This technique is FAR WORSE THAN FREAKINGTSUKUYOMI!!!
Meta-example, the 'Naruto is a gateway anime' copypasta. It's to the point that it became one of the banners in a certain imageboard.
When Itachi finally dies, his face smacks into the wall as he falls to the ground. This has pretty much become a meme of "Itachi Style: Facewall" when something is completely ridiculous.
One joke for the huge amount of Ho Yay between Sasuke and Naruto is that Sasuke is SasuGAY for Naruto.