If you are as confused as I was when I first tried to watch this show, you will need this.
Neon Genesis Evangelion
This is the original anime series. It consists of 26 episodes airing between 4 October 1995 and 27 March 1996.
The first 24 episodes are relatively comprehensible. Episodes 25 and 26, however, consist of extremely obtuse psychobabble and are, at the very least, unenlightening. A serious conclusion they do not provide - hence everything that follows.
This is a 60-minute re-edit of the first 24 episodes of Neon Genesis Evangelion. It has a few new scenes added.
This is a re-edit of Death without those new scenes.
This is a re-edit of Death with the new scenes and a brief image of Adam implanted into Gendo's hand, plus a few small cuts.
This is the first 27 (of 40) minutes of an entirely new animation intended to follow episode 24 of Neon Genesis Evangelion. It was cut down due to time constraints.
Evangelion: Death and Rebirth
Released 15 March 1997. This is a movie spin-off of Neon Genesis Evangelion consisting of Death and Rebirth put together.
Neon Genesis Evangelion director's cut
This is episodes 21, 22, 23 and 24 of Neon Genesis Evangelion with the extra scenes from Death edited in.
Episode 25': Air / Love Is Destructive
Note the apostrophe. This is read as "episode twenty-five prime". This is the full, 40-minute new "episode" of Neon Genesis Evangelion, of which Rebirth was just the first 27 minutes.
Episode 26': My Purest Heart For You (Sincerely Yours) / ONE MORE FINAL: I need you.
Note apostrophe again. This is a second additional "episode" of Neon Genesis Evangelion. Episodes 25' and 26' are intended to "complement" the original episodes 25 and 26 of NGE, and do not necessarily contradict them.
The End Of Evangelion
Released 19 July 1997. This is a movie consisting of Episode 25' and Episode 26' put together.
Revival Of Evangelion
Released 8 March 1998. This is a movie consisting of Death(true)2 and The End Of Evangelion put together.
So what should I watch?
Watch all of episodes 1 to 26 of Neon Genesis Evangelion, including the director's cuts of episodes 21 to 24.
Then watch Revival Of Evangelion, and you're done.
Hope this helps.