A non-Jew may not become a Nazir but women and servants may become Nezirim. (1)
A master may force a servant who became a Nazir to drink wine, but he may not force his wife who is a Nezirah to drink wine. (2)
If a non-Jew takes upon himself the Erech of a Jew it is not binding, but if a Jew takes upon himself the Erech of a non-Jew it is binding.
A non-Jew inherits his father but he is not obligated to honor his father and mother.
A non-Jew is not susceptible to becoming Tamei.
A non-Jew does not inherit a servant that belongs to his father.
R. Yochanan says that it is a Halachah l'Moshe mi'Sinai that a father may make his son into a Nazir. (3)
A BIT MORE
1. Even an Eved Kena'ani (a non-Jew) may become a Nazir.
2. Unless he annulled the Nezirus on the day that he heard it.
3. Reish Lakish holds that it is mid'Rabanan for the Mitzvah of Chinuch.
A NON-JEWISH NAZIR
The Gemara suggests the possibility that a non-Jew may become a Nazir but he does not bring the Korbanos of a Nazir. The Netziv explains that even if a non-Jew would not be obligated to bring the Korbanos of a Nazir however he would not be allowed to drink wine until Korbanos are brought for him by a Yisrael.
If a non-Jew vows that he is taking upon himself his Erech or the Erech of Ploni it is meaningless. If a Jew says that he is taking upon himself the Erech of a non-Jew he must give according to the age of the non-Jew. (Rambam Hilchos Erchin 1:6)