Campaign ideas
There are various possibilities. For instance, what about the dwarven Rings? I think Sauron recovered four of them, and three were taken by dragons. So what happened to those three? Apparently, only a powerful dragon's fire could damage a Ring of Power -- what if one of the Rings had survived? Did all Middle Earth dragons breathe fire? What if one had been stolen by an ice dragon? A campaign could focus on the quest for the hoard of such a dragon, with the minions of Sauron or Saruman also searching.
Then there are other opportunities. The adventures of the Fellowship weren't the only things going on during the War of the Ring. Mirkwood saw heavy fighting, as did Lorien and Erebor. The defence of the Lonely Mountain or the assault on Dol Guldur would make for interesting campaigns.
And then there are a lot of blanks in the book. What happened to the refugees in Rohan after Theoden and Eomer went to war? Was there peace immediately after Helm's Deep, or would there have been call for a group of heroes to scout out safe places, fend of attacks, and generally keep the commoners safe and calm?
If you want to give the party the feeling that they are contributing significantly to Sauron's defeat, let them form a vital distraction from the events around Minas Tirith and Frodo's journey. A large part of Sauron's strength was sent north to Erebor and Mirkwood -- victory there would have given him enough strength to defeat the forces of Gondor and its allies. Or maybe, once the PCs are powerful enough, allow them to find a palantir, so that they can upset him much like Aragorn did.
Anyway, the events leading up to Sauron's defeat are so vast that there's always room for a group of heroes. And whether you want to change the events of the books or not is entirely up to you, of course.
