Sequels that could be stand-alone movies...

[ulthar]

EVIL DEAD II: DEAD BY DAWN kinda sorta qualifies.

I'd also argue that the FRIDAY THE 13TH franchise pretty much fits.  I saw 2 before I saw the first one and really did not have any trouble figuring out there was a deranged guy killing teenagers.  The bit with Jason's mom was pretty self-explanatory.

When I finally did see 1, I did not think, "Oh...so THAT's what I didn't understand" or anything.

I don't think this applies to HALLOWEEN, though.  I also saw 2 before 1, and when I saw the first one, I DID make connections for things missed (or misunderstood) in 2.

[zelmo73]

Robert Rodriguez' silly Mexican live-action Mexican cartoon fantasy Desperado (1995) is supposed to be a sequel to El Mariachi (1992) but while it is more of a remake of the first movie than anything else, the two are completely independent of one another. Plus, the first movie didn't have Salma Hayek's nude scene, which is really the only reason to watch Desperado (1995) in the first place. 

[WingedSerpent]

EVIL DEAD II: DEAD BY DAWN kinda sorta qualifies.

I think a better example would be Evil Dead (I & II) to Army of Darkness.  AOD is more of a fantasy with some horror elements then what the first two were.  Really only a few names and items connect it to the other two movies.