Praise be to Allaah.
The word Sunnah has two meanings:
the path of guidance, which is the meaning in many ahaadeeth, such as the words of the Prophet (peace and blessings of Allaah be upon him): Whoever turns away from my Sunnah has nothing to do with me.
What the scholars of usool and fiqh call mustahabb (encouraged), which are deeds for which the one who does them will be rewarded, but the one who does not do them will not deserve to be punished for that. Examples include al-Sunan al-Rawaatib (Sunnah prayers which the Prophet (peace and blessings of Allaah be upon him) did regularly), Salaat al-Duhaa and so on.
Therefore, a person will not be punished for not doing things which are Sunnah in the second sense. With regard to the first definition, this is not the case, for these are divided into things which are obligatory (waajib) and things which are supererogatory (naafil).
Sunnat al-Fajr and al-Witr are Sunnah Muakkadah, prayer which the Prophet (peace and blessings of Allaah be upon him) never omitted to do, whether he was travelling or not.
Letting the beard grow is an obligation (waajib); it does not come under the category of Sunnah as defined by the fuqahaa. Whoever shaves his beard is imitating the Majoos (Zoroastrians), going against the Fitrah (natural disposition of man), and changing the creation of Allaah.
The one who neglects an act that is an obligatory Sunnah will be punished; the one who neglects a mustahabb Sunnah will not be punished, but he is missing out on a great reward and the chance to make up any shortfall in his obligations (waajibaat), because on the Day of Resurrection, any shortfall in his obligations will be made up from his Sunnah actions, if he has any to his credit. Doing Sunnah actions is also a means of maintaining the practice of waajib actions.
The scholars also use the word Sunnah in contrast to bidah (reprehensible innovation) and say Ahl al-Sunnah (the people or followers of Sunnah) to distinguish them from the followers of misguided kaafir sects such as the Jahamiyyah, or innovators who are not kaafirs, such as the Asharis and others. The Sunnah in this sense has to be followed. Following the way of Ahl al-Sunnah is obligatory, and whoever departs from their way is doomed. Imaam Maalik (may Allaah have mercy on him) said: the Sunnah is like the ship of Nooh: whoever boards it will be saved and whoever stays behind will be drowned.
For more information, please see Question #1189; for the ruling on shaving the beard, please see Questions # 3440 and #604.
And Allaah knows best.