This is a matter that I've myself have been trying to figure out. Indeed, this is a mojor topic and lots of things would probably have been changed.
In my opinion, I think that Gandalf would probably have sent Pippin with Frodo and Sam and he would've given them directions. Aragorn, Legolas and Gimli would've went to Rohan and Boromir (see as Gandalf would have been there to stop Frodo from leaving and Boromir from dying) and Merry would've gone to Minas Tirith. Also, seeing as Glorfindel prophicised that "no man would kill the witch king", I think Eowyn would still have gone to Minas Tirith. As for the breaking of Saruman's staff breaking, I think Gandalf would still have enough power to break it and Theoden would probably still have died. Another thing, if Boromir did go back to Minas Tirith, Denethor would not have gone crazy.
But like I said, this stuff is only my opinion. Hope no gets offended.
Glirdy 