Superman III
*raises hand*
That was me who voted for #3. I do think Superman 1-2 was better than the schlock that came after it, but I find myself still watching #3 even now. The others are good, but I can't seem to watch them over and over. But #3 has Richard Pryor, some crazy villians who aren't superpowerful or masterminds, and a computer that tries to take over the world. It's wonderful cheese with some really heroic scenes too.
To help make the case:
In #1 Lex knows that Superman cannot beat two nuclear missiles, only one. So Superman must -stop time- to actually save both the West coast and his newfound love. This seems more of a plot device than any real moral victory. [but I will admit it fits into the 1st film as a continual discovery of his powers]
In #2 Superman fights three supervillians each nearly as powerful as himself. In the end, he beats them through quick thinking and a bit of deception. Not as Deus Ex Machina as the first film, but deception has never felt like Superman's style to me.
In #3 however, Superman's enemy, his real enemy, is his himself. Before he can try and defeat the two millionaire villians he must face the horror of what he has let himself become. This is played out, it seems, as a metaphor of ego vs. alterego. I'm not even sure if what we see on screen is what really happens in the *real* world. It's more through Superman's/Clark's own point of view(s).
It's in this crucial scene where the common man, but also the one who fights for truth and justice, must overcome the all-powerful, yet all-corrupted superman. I know that watching it, this scene can come off as full of cheese, but the victory of Clark (finally a real superhero again) is the climax of the movie. I still feel pride swell in my chest when I watch it.
The rest of the film is just denouement, but still pretty fun. In a nice parallel to the first fight, the villians fail in the last scenes because of their own greed and corruption. The power they hope to harnass (the "super"computer) actually becomes a monster and takes over one of their number.
[this is actually one of the scariest movie scenes from childhood. The act of that computer taking over and transforming that harridan

of a woman henchman always scares the bejeezus out of me.]
So, it seems Superman is just there to mop up the after effects. But in reality he had already won the fight. No real comic book style fight scenes, but still pretty heroic in my mind. The layer of velveeta over it all just adds the the fact that it really needs to be viewed more as camp than as serious drama. But cheese ran through every Superman film.*
So, uh, yeah. Superman III rocked!
*(I cannot really say with Supergirl, though, as I've never seen the film)