This is an issue on which scholars have differed because of their differences in looking at the practice of the Prophet (peace be upon him). However, all of them seem to agree that one should pray the two rak'ahs of sunnah before fajr and the witr salah. As for other strong sunnahs there are two views: One should perform the above two prayers; and one skips the other sunnahs a second group says: One should pray them; a third group is of the view that one should pray them while being settled and leave them while on the go or taken up by the travails of the journey.
The third view seems to be striking a middle position as it reconciles the various reports on the issue.
Both Bukhari and Muslim report on the authority of Ibn Umar that the Prophet was not in the habit of praying sunnah prayers while traveling. This is the basis for those who rule that one should leave the sunnahs during travel except for the witr and two rak'ahs of fajr. They further reason that there is no point in shortening the prayers while travelling and yet insisting on praying all the sunnahs.
The second group, however, relies on another set of traditions, which seem to indicate that the Prophet (peace be upon him) sometimes did offer sunnah prayers. They also rely on the famous tradition reported by both Aishah and Umm Habibah that the Prophet (peace be upon him) said, "whoever is consistent in praying twelve rak'ahs of sunnah, Allah will build for him or her a mansion in paradise." They took this to be applicable to all times.
The third group interprets this discrepancy saying that the Prophet (peace be upon him) did not pray the sunan (except for the witr and the two rak'ahs of sunnah for fajr) while he was on the go, while he did offer them while he was settled.
The third position seems to be the preferred view to follow as it explains the variant reports reported from the Prophet in regard to this issue.
In conclusion, one should never skip the witr prayer or the sunnah of fajr. As for the others, one may choose to do them or skip them; it, however, good to do them if one is settled.