Colbert Bump: The airing of Eva 1.11 on Toonami garnered nearly one million viewers and lead to Eva 1.11 taking the #1 spot on Amazon's top selling anime list after its airing (with Eva 2.22 not too far behind).
Technically, the title itself, Rebuild of Evangelion, is a nickname that just stuck very hard because Anno and other official sources used the term a lot during the promotion for the first film; from all appearances, the term actually refers to the simple act of remaking the series. Considering the movies are simply titled Evangelion (or Evangelion New Movie Version), it's doubtful that the phrase was meant to refer to the movie series itself. The Evageeks forums tried to get rid of it by renaming the sub-forums from Rebuild of Evangelion to Evangelion New Movie Version, but then changed it back.
"Weva", short for "Wevangelion" has been used to refer the movie occasionally; see Xtreme Kool Letterz on the main page for why.
The formal names each Angel (well, what Seele calls them: "Sachiel", "Ramiel", etc.) were only revealed towards the end of the original series, during a quick review scene (and by quick, we mean blink and miss quick). As this hasn't happened yet, the two new entirely new Angels don't have formal "Angel names", so have been often referred to be fan nicknames: #3 has "Tunneliel", and #7 has been variously referred to as "Clock Angel", "Clockliel", etc.
Mari's battle with Zeruel is often just referred to as "ZA BEASTO", after the password used to trigger Unit-02's "beast mode".
I Knew It: Before the release of actual news of 3.0, there was a fake movie poster of Shinji sitting alone on the staircase◊ from the first two posters. Considering the darker tone the movie turned, it turns out this mock poster was scarily accurate.
Loophole Abuse: A meta-example regarding the Mexican release of the films: The Mexican distributors of the films managed to avoid having to dub the films to Spanish as required by Mexican laws by showing the films as art films and as such, those films are not required to be dubbed. It does help the films are Japanese and also the fact the films are showed as a part of the 400th anniversary of the relations between Mexico and Japan. On the other hand, the films will be released with subs and a dub on DVD, since it's required by law and the mentioned loophole will not probably work in this case.
Lying Creator: Goes hand in hand with Trolling Creator, but it's clear that Anno and the rest of production staff can't be fully trusted, from Mari's "no psychological issues" line, to a very high usage of Never Trust a Trailer and whether or not the series is actually a remake or a sequel.
Case in point, in the preview for 3.0 at the end of 2.0, only one thing is accurate: Asuka's eye-patch.
Throw It In: In Evangelion 3.0, Shinji's silent coma near the end of the movie was a result of Megumi Ogata, his VA, being too distraught to continue reading her lines after Kaworu's death.