Went to start my '76 the other day, and upon turning the key, the engine tried to turn but didn't. No biggie...that happens all the time. Try again! Nothing, then a small "snap" noise and smoke from the battery compartment.
I look back there and the positive batter connection is smoking, and the cable is almost too hot to touch. I let it cool off and clean both the connector and the post (on the battery) because they were both not perfectly clean. Once they're both pristine, i put it back on. Turn the key, nothing. More smoke. But this time, the + terminal melted. Hmm....that's not good.

I replaced it and tried starting again. It turned just ever so slightly. Again, turned a little more, and finally it started.

What could have been causing this? Bad starter? That's my first guess....i've had issues with it not wanting to start in the past, and am likely going to replace it regardless, but I wanted some expert opinions first ;-)

Thanks in advance,
Brian

Either a bad solenoid/starter, or the cable itself. Replacing the terminal at the battery may have helped, but if the cable itself is heavily corroded inside, it can do stuff like that.
Usually, localized heat like that means the connection is bad/loose/corroded, and drawing too many amps...that's what causes it to get hot...it's literally welding itself. If the cable was hot all the way from one end to the other, then I would think the starter was the bad boy here.
I'd maybe have the starter checked first, and then go for replacing the + cable from the batt. to the starter...and make sure the terminal that is made into the battery is not loose in there...it can happen

Once again, Joel is correct.  The side connectors (suck) on my '96 GMC broke in the battery and acted like there was a short in the fuse panel.  When shutting the vehicle off after a 30 min or more drive, it would make a zzzaapping sound and the lights would flicker, then go off.  It took me forever to figure it out.  When the side mounts break inside, it is darn hard to find.

Good Luck!

Follow your positive + cable from the starter to the battery and make sure there is not a break in the wire, causing it to ground. The + cable runs by the exhaust, transmission and drive shaft,  if contact is made because of a lose or missing wire clamp, it can wear down to bare wire. I Recently changed my + cable and found this problem - before it became a problem.
Post your results.
Good Luck!