Gandalf victorious
 

What do you think would have happened to the Fellowship's journey (and beyond) if Gandalf had defeated the Balrog on the Bridge of Khazad Dum and led the Fellowship out of Moria as Gandalf the Grey?

Heh. Well, it's all speculation, but I might as well do a little of it...

I believe perhaps Gandalf would have seen Boromir's temptation after Lorien easier than the others did and maybe would have talked him out of it somehow.

Aragorn wouldn't have built up so much trust in himself, as he was forced to lead the Company after Gandalf's fall. He couldn't clearly decipher what Gandalf would have wanted him to do, so the task was placed on him, giving him more confidence in his decisions, as all of his choices seemed to be the right ones.

Frodo wouldn't have been wandering off alone in Amon Hen in the first place with Gandalf there.

The stay at Lothlorien would have been much different, I presume.

One could go on, but I'll stop there.

:D Please go on!!!! :D

Well Gandalf did defeat the Balrog, he just ended up dying in the process. And it's a good thing he ended up dying. As 'the old' Gandalf would not have been able to handle Theoden nor Saruman:
Then as Letter 156 talks about it's Gandalf's sacrifice and obeisance to 'The Authority' that gets him sent back with some power uppage to deal with Saruman. As the old Gandalf would not have had the power to do so. So, had Gandalf lived and continued on with the Fellowship, he would have either had to die, and be sent back with some extra power, or I think a whole crap load of problems would occur. As Gandalf the Grey would not have been able to help Theoden nor boot Saruman from the Order.

The Quest would have failed far earlier if Gandalf had not fallen.

Remember that, shortly after leaving Lothlorien (where he had been taken shortly after awakening on top of Zirak-Zigal), Gandalf strove with the Dark Lord in thought. This is why the Sauron had trouble perceiving Frodo when he put the ring on at the top of Amon Hen. Had Gandalf (the White) not wrestled with Sauron in thought, Frodo's position would soon have been discovered.

Disagreed. The quest probably would have succeeded much quicker, though Saruman would have won Rohan I think.

I agree there was need for him to fall. This way he could be sent back as head of the Order, as what Saruman should have been, the one to lead the forces of the free people against those of Sauron.
As said in the UT, if Manwe sent Eonwe to the defeat of Melkor he would have also sent a spirit coeval in power with Sauron to his downfall, and by this Olorin/Gandalf is meant.
His rebirth with new powers was needed.
Of course he could have aided Sam and Frodo a lot, perhaps even save Boromir, but in the end I think it was for the best that he was initially defeated.

Rhod, and had Saruman won in Rohan half of the forces defending Minas Tirith would have been wiped out. No one would have come to Gondor's aid except perhaps the Dunedain...if they ever met up with Aragorn. Karen Wynn Fonstad estimates the forces during the Siege of Gondor were a little over 11,000 (this includes the Rohirrim). Looking at the numbers we are given in the text, this seems to be a relatively good guess. The Rohirrim set out with 6,000 men, that's over half of Gondor's forces. Gondor would have no chance of winning. There was no hope for a military defeat of Sauron, but the war itself still served a purpose, it kept Sauron thinking that someone in Gondor (that being Isildur's heir) had the Ring and was going to use it against him. Without the victory during the Siege of Gondor and the Battle of Pelennor Fields, which leads to marching an army to the Black Gate, the quest would have indeed failed.

I thought of the same thing first Boromir, but...I thought it might not really be correct. One could say that, had Gandalf survived his duel with Durin's Bane, the Fellowship would have achieved its goal in the end but using another plan. Perhaps Gandalf knew some obscure pass in the mountains leading to Mordor, or perhaps he could make sure that the Orcs would not detect them so easily.
I agree that it was better that he died, many lives were saved through his rebirth, but still perhaps the quest would have been achieved even if he wouldn't have died.
Sauron expected the Ring to go to Minas Tirith so if the Fellowship managed to enter Mordor unseen they might have chances to make it to Mount Doom and destroy the Ring. ;)

You could always look at it this way. They way things happened was the way they were meant to happen (or the way Tolkien wanted them to). All of the possibilities could have happened...but it would have affected everything that came after it.