i have found myself wondering this same thing as well as others. and i have been involved in some other "what if" threads. and one thing that i have been told and have given thought to is the fact that everything happpens for a reason, and everything has a purpose. even the tinyest detail has some sort of importance.
for something as big as Gandlaf dying to be changed would change the entire story. you wouldnt have Gandalf the white. the fellowship would still be together. its hard to say where the story would go because of how huge the change would be but i personally think as for Rohan it would have probably been defeated in Edoras and then at the battle of Pelanor Fields they wouldnt have been able to help, and they played a big part in that. the witch king might not have been defeated as a result of Eowyn not being there. as for Aragorn and Boromir, they would have prolly continued to Minas Tirith and gone to help hold Osgiliath and maybe over run since Gandalf wouldnt have been there to drive away the Nazgul because he was away in Mordor with Frodo. the Hobbits and Gandalf would have continued to Mordor and i have no idea how they would have gone because Gandalf prolly would have gone a totally different way. they prolly wouldnt have found Gollum and then who knows who knows if the ring would even be destroyed then, because it was an accident that it even happened in the first place. as for Legolas and Gimli its hard to say where they would have gone because if they didnt have to rescue Merry and Pippin they prolly wouldnt have gotten so close with Aragorn and might not have been willing to follow him to death.
so really its hard to say anything other than the story would be totally different.
sorry this is so long but i got started and once that heppens its hard to get me to stop.