: There is, of course, no "right" answer, but I'm curious about how many different perspective people may have on this. I suspect he would have gone on to Minas Tirith and sacrificed himself somehow, but then his death would be less tragic.

Well, I think that this is how things would have gone down... had merry and pippin not come along

At the ard gallen(is that the right name?) on the rivern Anduin, boromir gets enraged at frodo with lust for the ring, the others go looking for frodo, Boromir wanders aimlessly still downcast after he realised his fault with frodo. now here it could go one of two ways... one in his aimless wanderings boromir runs into the orcs anyway and is killed after a desperate fight but dies unredeemed because he was not giving his life to save the hobbits and it was not a particularly noble deed, he just got bushwaked by some orcs.
The other branch is that boromir doesn't run into anything, or goes with gimli and legolas and lives past that day... I think that frodo would still have gone off with just sam and Aragorn and the others would have missed him because aragorn would still have gone to the high seat on Amon Hen(or was it the other Amon which I can't remember at the moment?) Anyway, after these events is when merry and pippin's absence would have felt its main punch... Aragorn, Gimli, Legolas and Boromir would have gone directly to minas tirith, obviously having no one to pursue into rohan they would have no other logical choice.
Thus merry and pippin do not come to fangorn, perhaps gandalf rouses the ents but it probably would not have been as timely as it was had merry and pippin been involved. Also Aragorn, Gimli and Legolas are not present in rohan for the rousing of theoden or the battle of helms deep, this could have an affect in helms deep because the three great hunters had quite an effect in that battle and their abscence I think could have swayed the tide just enough... Saruman would still have been destroyed I think by the ents but rohan's strength would have been greatly deminished and perhaps both the king and eomer would have been killed leaving them no strong leader to bring them to gondor's aid...
Now Gondor would recieve much less aid at pelanor from Rohan, and Aragorn would not have ridden the paths of the dead thus the corsairs of umbar would take the souther provinces rather than aragorn sailing up the river with reinforcements so the battle of pelanor fields would probably have been lost on those accounts alone.. however, there is more bad news I think in this story... I think had boromir survived to come to minas tirith it would have been disasterous for aragorn and Gandalf, Boromir I think undoubtedly would have sided with his father and would have opposed aragorn's claims when it came right down to it. Aragorn would have little or no support either and thus would have no real chance to claim his throne because the only friends he would have in minas tirith would be gimli legolas and gandalf, which vs. the entire tower guard and army of gondor would not have avialed to take the throne so at best aragorn and company would have had to have taken a subordinate role to denathor and boromir if they wished to remain free and in minas tirith. Furthermore I think that Boromir as his father would have become more twisted with time and not found the redemption he did in saving merry and pipin, thus I do not think it is inconcievable that he would have plotted against aragorn (using him to fight for gondor while necessary but then getting rid of him).
I think sam and frodo would still ahve completed the quest of the ring but they would have died in the erruption as there would have been no march by aragorn to the gates of mordor and thus no army of eagles... so I think, that had merry and pippin not come along the ring would have been destroyed but gondor would have been laid waste and to a lesser degree rohan too, saruman overthrown, but the entire fellowship except for gandalf are dead and there are still hordes of unfriendly orcs and men who are still alive roaming in gondor with out souron to bind them together.

:) that was fun