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So Holden Pike sorta ret-conned this into a "guilty pleasures" thread instead of a "secret favourite movies" thread, so I'll say this: the first half of Digimon: The Movie (2000). I was never much of a digimon kid, but dammit, (the first half of) this movie was good. The last half was crap. But the first half was good! The whole plot of the world being taken over by an Internet-based digital digimon (aren't they all digital? Isn't that why they're called digimon?) was super cool, and the way they had all the characters come together from different locations through the Internet, cut off from telephones save for a monotonous phone-tag system was a unique situation. Then, with the whole world watching, when they finally take him on in cyberspace... still gets me a little welled up. Though the whole "merging with your digimon thing" was kinda stupid, but I'm willing to let that one go.
And of course it only goes downhill from there... but, the director (or some other main guy involved with it,) went on to create Summer Wars (2009), a feature-length and much better produced anime movie with the same plot of the first half of Digimon: The Movie! So I'd advise just watching that if anything I just described seemed remotely interesting, because Summer Wars really was a phenomenal movie. But anyways: in terms of "secret favourite" movies, I will have to say The Poughkeepsie Tapes (2007). Now, I wouldn't say this is an irredeemable movie, or even a terrible one. Most people seem to agree it was poorly produced and the acting was sub-par, but honestly I really enjoyed it. And that's why it's my "secret favourite." It's torture-porn set to the style of a mockumentary. I don't think it even had an official DVD release, aside from maybe some DVDs sold off of its website. It definitely didn't have a theatrical release, it was just screened at a few film festivals as well as being hosted on YouTube for awhile. But anyways... definitely not the type of film I would bring up as a personal favourite with someone I'm meeting for the first time. I'd be fine with mentioning Saw (I really liked Saw as well,) but not this.