Similar to other symbols like itself, such as the Irish Claddagh ring, the promise ring, the Star of David and the CTR ring, the cross symbolizes a belief in one thing, is simplistic, shows a sign of commitment and has a rich history.

Irish Claddagh ring
Traced back to 16th-century Ireland, two hands grasp a heart, as a crown sits on top of the heart, creating the famous, yet simplistic Irish ring. Originally given as a gift from a slave to his master, the ring became a symbol of commitment used in wedding ceremonies in Ireland. Today the ring continues to symbolize commitment, but also friendship. Although the Claddagh ring has similarities to the crucifix, the ring is reserved for one culture — you won’t see an Italian citizen walking around wearing it. Also, it shows no devotion to God or Jesus Christ.

Promise ring
Like the crucifix, the promise ring symbolizes commitment, devotion and love; has more than one meaning; and is popular. Used as a way to show devotion to one before engagement, the promise ring has become a popular part of American culture. The promise ring is also given to virgin girls by their parents as a symbol of their promise to stay chaste until marriage. Unlike the crucifix, the promise ring is worn by anyone of religious or non-religious beliefs.

Star of David
Used to identify Jews in WWII, the Star of David has become a symbol of their culture. Similar to the crucifix, some sects of Judaism have rejected the use of the Star of David. Interestingly enough, those who are not Jewish, such as Muslims and Arabs, use the Star of David to symbolize different fundamental elements of their beliefs.

CTR ring
The CTR ring, which stands for ‘choose the right,’ has become a Latter-day Saint cultural symbol. The three simple letters enclosed in a shield have come to represent the basic belief of The Church of Jesus Christ of Latter-day Saints that members have the right to choose and reminds them to make good choices. Similar to the crucifix, the CTR ring represents a religious belief, yet unlike the crucifix, the CTR ring is only used to identify one sect of Christianity.

Sources:
www.wadsworth.com/religion_d/special_features/symbols/crucifix.html
mb-soft.com/believe/txn/cross.htm
www.newadvent.org