Suzumiya Haruhi no Yuuutsu (The Melancholy of Haruhi Suzumiya) is easily one of my all time favourite scifi anime series. It has everything: a fantastic premise, a complex plot, great characters, and, you guessed it, time travel! The series was originally broadcast out of sequence which added to the impact of the story. When the creators decided to extend the series with an additional 14 episodes that would be interwoven with the original episodes, fans were ecstatic.
Unfortunately, the 2009 series was very disappointing, mainly due the Endless Eight arc, a series of repeating episodes in the style of Groundhog Day. This type of repeating story has to be carefully crafted otherwise it just gets, well, repetitious, but the creative team totally dropped the ball on Endless Eight.
With Suzumiya Haruhi no Shoushitsu (The Disappearance of Haruhi Suzumiya), a theatrical movie released last year, the series creators have fully redeemed themselves. The story is richly detailed (at the cost of being a little slow moving), and finally confirms how Kyon, the male lead character, feels about all the crazy stuff that has happened since meeting Suzumiya, the female lead character. He is given the choice of living a normal life or restoring the crazy world in which time travellers, aliens, and espers are real. Which would you choose?
You must watch the 2009 series before the movie as it contains many references to the series, but you can safely skip most of the Endless Eight episodes, if you get bored. ^_^ However, I highly recommend that you first watch the original series in the out of sequence broadcast order to get the full impact of how creative the series was.