Hadrat Zaid ibn Arqam Radi ALLAHu Ta'ala Anho reported that the Messenger of Allah has said, “Whoever does not take something off his mustache is not one of us (not on our path).” [Sunan Nisa'i, Vol 2, Page 274]

Sayyiduna Abu Hurayra Radi ALLAHu Ta'ala Anho reported that the Holy Prophet Peace and Blessings be Upon Him said: “He who does not shave off the hair from the abdomen and does not cut his nails and does not trim his mustaches, is not of us”. 
Sayyiduna Anas Radi ALLAHu Ta'ala Anho reported that the maximum exemption for shaving off the hair from the abdomen and armpit and for cutting nails and for trimming the mustaches is forty days. [Sahih Muslim]
Hadrat Abu Huraira Radi ALLAHu Ta'ala Anho reported that the Messenger of Allah has said, “Cut the mustaches and let the beards grow long; (by doing this) do the opposite of the fire worshipers.” [Sahih Muslim, Vol 2, Page 129]
Sayyiduna Abu Hurayra Radi ALLAHu Ta'ala Anho reported that the Glorious Prophet of Islam Peace and Blessings be Upon Him said: “Five things are from the traditions of the Prophets of the old: circumcision, removing the hair below the navel, trimming the mustaches, cutting the nails and removing the hair from armpit”. [Bukhari, Muslim]

IMPORTANT NOTES:
1. Many of our Muslim brothers have opted to make their beards into a fashion and have a ‘stylish’ effect to it. Many completely shave it off and some leave a bit on the chin. Some keep their beards only 2 fingers long, and believe that they’re following the Shari’ah, despite the fact that those who shave all of their beards and those who shave it to less than one fist are all the same in sin in the eyes of Shari’ah. It has been stated in Bahar-e-Shari’at:
To grow the beard is the Sunnah of the prophets. To shave it all or less than a fist is Haraam.

Hadrat Shaykh ‘Abd al-Haq “Muhaddith-e-Dehlwi” has stated:
To shave the beard is Haram, and the way of the English, the hindus and monkey-dancers. It is wajib to leave the beard to grow to one fist. Those fuqaha (scholars) who have stated that to keep the beard one fist is sunnat, then this is not because according to them to keep the beard to one fist is not wajib, but in fact “sunnah” in this context means the Islamic way, or because the wujub (necessity) of keeping a beard one fist has been proven from the Sunnah (the ahadeeth – prophetic traditions of the Beloved Prophet), just as the Eid prayers have been called sunnat, despite the fact that they are wajib.

It has been stated in al-Durr al-Mukhtar (Vol. 2 Pg. 116), Radd al-Muhtar (Vol. 2 Pg. 117), al-Bahr al-Ra’iq (Vol. 2 Pg. 280), Fath al-Qadir (Vol. 2 Pg. 270), Tahtawi (Pg. 411) that:[and the words quoted here are of Tahtawi’s]
According to the unanimous opinion, to shave the beard less than a fist as is the way of some westerners and effeminate persons who are fond of make-up like women, is not permissible. As regards shaving whole of the beard, then this is the way of the Jews of India and the fire-worshippers of Iran.
2. Hadrat Sayyiduna Imam al-Ghazali Radi ALLAHu Ta'ala Anho said:
If in a battle the dead amongst the Muslims and non-Muslim become mixed then every corpse will be recognized by their trimmed mustaches and beards (not less than a fist). Those that possess trimmed mustaches and beards will be bathed and dressed according to the Muslim rites and Salat-ul-Janazah read over them while those not possessing the above signs will be buried like the non-Muslims i.e. Without bathing and dressing and Salaat-ul-Janazah.
3. It is permissible to grow the beard more than the Shari’i limit of one fist. However - according to our Imams and scholars - to let the beard grow such that it becomes extremely out of proportion, and which shall be a incite people to point fingers and make humor out of that person, is offensive and disapproved of. [Lum’ah al-duha fi I’fa al-Luha (Imam Ahmed Raza Khan), Fatawa-e-Radawiyyah, Vol 22, Pages 571/573]