I wish the Romans had thought the entire Arabian peninsula (well, the coasts) worth conquering. Mohammed's ancestors (one or more of them) might have gotten whacked, and that would have had a positive impact throughout history.
Alexander the Great was making preparations to conquer Arabia shortly before his death.
As to the Romans, I've read that Augustus was going to send his adopted son (and grandson by blood) Gaius on some sort of Arabian/Oriental campaign, but the one source I've read this is quite vague, so I don't know if it was meant to be against the Parthians (which seems a bit doubtful sense Augustus had demanded and received a favorable peace from them yrs earlier) or into the Arabian peninsula. Or it could have been intended for a more modest slice of Arabia, like the one one his legates failed to take and which Trajan finally did absorb into the empire. But whatever the plans were, they ended with Gaius' death.
Who knows how history would have been altered, but certainly its a shame that a united, powerful Roman Empire did not last long enough to face the successors of Mohammad. At the very least, they probably could have stopped the spread of Islam to the West.