Neon Genesis Evangelion: The original anime series, which ran over a course of 26 episodes from October 1995 to March 1996.
Evangelion Death And Rebirth: Feature-length film released in March 1997. Consists of the titular two parts:
"Death", which is essentially a Clip Show using material from episode 1-24 with some entirely new scenes added in. Some of these scenes were later included in the "Director's Cut"/"New Production Cut" version of the anime.
"Rebirth", which consists of the first 25 minutes of The End of Evangelion.
The End Of Evangelion: Feature-length film released in July 1997. Consists of alternative versions of the anime's episodes 25 and 26. Whether it is meant to replace or complement the original ending remains a hotly debated issue in the fandom.
Rebuild of Evangelion, a retelling consisting of four new animated movies which is currently in production. The first film was released in Japanese cinemas in September 2007, and as of the second film, Rebuild has become a full-blown Alternate Continuity. Although it is by no means Lighter and Softer, character angst/personality issues aren't quite as extensive, and some arrows point to an actual upbeat ending instead of the grim yet Bittersweet Ending of The End of Evangelion.
The manga version, written and drawn by character designer Yoshiyuki Sadamoto, which tells the same story as the anime but with a number of changes. It finally finished its run in June 2013note February 2015 for the English version, after starting out as promotion material for the upcoming anime back in December 1994.
Neon Genesis Evangelion ANIMA, a Light Novel series set in 2018 in an alternate continuity where Third Impact never happened. It's been described as if Anno made Evangelion like a Gundam show. It contains (among other things) Evas duking it out in space, three Reis (again), and Fanservice. Available here and here (untranslated, unfortunately, despite the efforts of the Translation project).
Neon Genesis Evangelion Girlfriend Of Steel (also known as Iron Maiden), a Visual Novel released in 1997 in the style of an episode. This adaptation introduced Canon Foreigner Mana Kirishima, who went on to reappear some years later in Shinji Ikari Raising Project.
Neon Genesis Evangelion Girlfriend Of Steel 2, another Visual Novel released in 2005. Despite its title, it is not a direct sequel to the first Girlfriend of Steel but more of a Spiritual Successor which takes place in the Alternate Universe from the anime's Episode 26. It later got adapted into the Angelic Days manga.
Neon Genesis Evangelion: 2nd Impression, a Visual Novel with several parts styled like an episode each. Introduced Canon Foreigner Mayumi Yamagishi, a Shrinking Violet described by fans as the female equivalent of Shinji.