Sly did indeed audition for the role of Han Solo, and picturing the wise-cracking jet pilot as something more of a Rocky-like lummox is amusing to ponder. Stallone was, however, quickly looked over by George Lucas, and he never got a callback.
When Attack of the Clones was in production, there was a bitter fight in Hollywood as to who would play the young Darth Vader, in the pre-mask days. The pouty-lipped Ryan Phillippe was already a known quantity in the biz, and got so far as readings with other actors, before he lost the role to Hayden Christiansen. Phillippe may have been too young, or perhaps not “dark” enough.
Harrison Ford may be irreplaceable in people's minds as Han Solo, but James Woods would have, I think, been an improvement. Han Solo is a flip, wisecracker, right? Who better to give off a cynical attitude than the excellent James Woods? He auditioned for the role, but was turned down.
Why she was not hired is anyone's guess, but Karen Allen – pre-Animal House – did indeed audition to play Princess Leia, long before she entered the action/adventure canon as Marion Ravenwood in Raiders of the Lost Ark. I feel she would have made a more human, earthier version of the character, as Carrie Fisher is, comparatively, daintier and prettier.
One can find video evidence of Kurt Russell's audition online, meaning he came close to landing the role of Han Solo. I adore Kurt Russell, as does every right-thinking person, but his audition was a bit awkward, and he is perhaps too genial and heroic to be the cynical sidekick of the series.
There was once a rumor that Carrie Fisher was up for the P.J. Soles role in Brian De Palma's Carrie, and Soles was up for Princess Leia, but Fisher was rejected on account of nudity. Fisher would have done the nudity, however, and the rumors are not true. The spunky Soles, however, did audition for Princess Leia. Had she landed the part, it would have made for a very different movie.
Yes, there was a time when Robert Englund was not known for horror, and was merely a struggling actor just like all his contemporaries. Englund auditioned for Solo, but was considered too young for the part, and perhaps not '70s dashing enough. Legend has it, though, that it was Englund who encouraged Mark Hamill for the role of Luke Skywalker.
The famed voice of Bugs Bunny, Barney Rubble, and a thousand others was once considered to dub over C-3PO's lines the same way James Earl Jones dubbed over David Prowse for Darth Vader. Blanc was, and is, a legend in the voice acting world, and there's no doubt he could have come up with an iconic and great vice for the fey robot. Lucas eventually let actor Anthony Daniels read his own lines.