In my minhag (and I believe it's minhag Ashkenaz), unmarried men do not wear a Talis Gadol (only a Talis Katan).
Why is this so?
In D'varim 22, the pasuk commanding placement of tzitziyos on 4-cornered garments immediately precedes the pasuk describing/commanding getting married. The juxtaposition gave rise to the minhag of simultanaizing these two acts.
Extracting instructive meaning from the juxtaposition of two verses is universally acceptable as a method of interpretation only in D'varim. The example used by the g'mara to prove this includes one of the aforementioned p'sukim. In this issue of Yeshivat Har Etzion's Daf Kesher, the topic is addressed. Its mention is attributed to the Sefer Hamanhig, on whom the Mishna B'rura asks exactly @jake's question in the comment below: How could it be that a mitzva from the Torah is pushed off beyond the age of bar mitzva?
It is suggested that although an interesting symbolic connection exists between wrapping oneself in a talis and protecting one's wife or imitating God's ways, citing the pasuk is intended to be a postfix hint and not an ab initio source.
(Also see this Satmar publication for extensive treatment of the same question: פרי תמרים)
The B'nei Yissachar says that kabalistically, a Talit Gadol draws down an Or Makif (Transcendent Light). This can only be drawn down when a person is joyful (with Simcha Shel Mitzvah). Since the Gemara says (Yevamot 62B) "A man without a wife lives without joy", and (Shabbos 152A) "The joy of the heart is a woman" an unmarried person does not wear a Talit Gadol.
(I found this in "Tzitzit - Halacha Lema'aseh")
There is no chiyuv to wear Tzitzis unless you are wearing a 4-cornered garment. That used to be what they wore in bavel, but over time the style of clothing changed. It became customary to specifically put on a 4-cornered garment so as to get the mitzvah of Tzitzis. It seems that the custom to wear a large 4-cornered garment was only adopted by married people, perhaps due to financial reasons.
Note that German-Jews do wear Tallesim before marriage, and I think R'Hershel Schachter also thinks its a good idea.