Lance Henrikson was almost the choice for the Terminator, as one of Cameron's plans for the character was that he wouldn't stand out in a crowd as much and be far more stealth-oriented than Arnold who is a wrecking ball in several scenes, throwing a guy out of a phone booth, crushing a bouncer's hand just walking into club noir etc and not even bothering to cover up his murders of the other Sarah Conners. Some concept art even has Lance, and even showed up in costume to some pitch meetings.
However the role went to Arnold and Lance was cast as Det. Hal Vulovich, the slightly more skeptical of the detectives who help Sarah out (but wind up being the Terminator's victims).
Some of the ideas of a thinner, "everyman" Terminator seems to have been some of the thinking behind the T-1000 though.
Of course there have been many "almost castings" but in general some of these probably wouldn't have changed the film that much (Like, I don't think Tom Selleck's Indiana Jones would've necessarily been that different), but something like Lance being replaced by Arnold seems to be a rare case where it would seem like a pretty different film.
Any other ideas?