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As for reboots and remakes.....
This is a little tricky, but I think the first movie of a rebooted series or a remake should be excluded and only the sequel should count.
Thus, Star Trek: Into Darkness would count, but not 2009's Star Trek.
Reboots and things can have their own countdown. THIS is a SEQUEL countdown.
But I totally think -- unless there's a case I'm not thinking about -- that prequels can be allowed. Especially if it's a prequel in the form of a sequel. Stupid example -- Puppet Master III. That's a prequel in the form of a sequel.
However, something like X-Men Origins: Wolverine... that I don't know. Because it's starting off its own separate storyline with a different title and everything. It's not a sequel to the other X-Men movies. Count you count it? Maybe.
The sequel stuff is messy -- HOWEVER -- Star Trek: The Motion Picture is not a sequel!