For Frodo, there were over 150 auditions. Jake Gyllenhaal (who is over six feet tall) was one but apparently Jackson and all really wanted a British actor. Elijah Wood sent in a home made audition tape that blew him away. Dominic Monaghan originally auditioned for the roll of Frodo and would otherwise have been cast in it instead of as Merry.
Numerous actors were considered for Aragorn. Daniel Day-Lewis, Nicholas Cage, and Russell Crowe were all approached but (thankfully) all turned the offer down. Stuart Townsend was originally cast but was unable to portray the character in the desired way (which is no surprise since he was less than thirty at the time), so Viggo was offered the role and was given less than two hours to respond. Fortunately he said yes.
Patrick Stewart and Sam Neil were considered for Gandalf. Jackson was very interested in having Sean Connery play a part, which the latter reports was Gandalf (though apparently it was actually Theoden… shows you how much the guy cared). He rejected it because he didn’t understand the plot or script. Jackson was also interested in having Tom Baker (the fourth Doctor in Doctor Who) take the role, but in the end Ian McKellen it was.
Orlando Bloom originally auditioned for Faramir but was offered Legolas instead. David Wenham was chosen for Faramir because of the slight resemblance to Sean Bean, who’d been cast as Boromir. Speaking of Boromir, Bruce Willis was very interested in the role but was rejected.
Finally, David Bowie really wanted to play Elrond. Of it Jackson said, “To have a famous, beloved character and a famous star colliding is slightly uncomfortable”. And, while Bowie’s filmography list is substantial, he did have a reputation for campy, cult films that weren’t to be taken all too seriously. Therefor, the younger Hugo Weaving was cast as the elf lord of Rivendell.