The word "Christian" occurs thrice in the Bible:
Acts 11:26 And when he had found him, he brought him unto Antioch. And it came to pass, that a whole year they assembled themselves with the church, and taught much people. And the disciples were called Christians first in Antioch.
Acts 26:28 Then Agrippa said unto Paul, Almost thou persuadest me to be a Christian.
1 Peter 4:16 Yet if any man suffer as a Christian, let him not be ashamed; but let him glorify God on this behalf.
The word reflects what others called them, not what the "Chrisians" called themselves.
In the centuries between then and now, the term acquired new meaning (for example, members of the church headquartered at Rome). After the Reformation, it came to mean members of churches other than Roman Catholic (for example, the eastern Orthodox Christians) and became the generic word for Lutherans, Calvinist, Wesleyan, evangelical, baptist, brethren, pentecostal, and other churches).
There was a period when, in churches that emphasized direct relationship with Christ as head of the body), the word Christian connoted the in-Christ-ness of one who trusted Christ for salvation and forgiveness of sin.
Today, the term refers to a broad cultural or ethnic background, or a category in a census or on a civil registration form or identity card. In certain circles in third world countries, the term refers to a cultural background in which greater permissiveness is found than in the stricter religions of the region (for example, certain branches of Hinduism). The question "Who is a Christian?" has its parallel in Jewish circles where the question "Who is a Jew?" has been discussed by various authorities. (See Being Jewish, the Jewish Virtual Library, Judaism 101)
If being a Christian is only a social, cultural or demographic category, the name rings hollow.
Given the hollow way the world around us understands the term, how should we as born-again Christians designate ourselves in our own circles, or to those seeking to know Jesus and to understand the Bible?
Consider the following terms, all of which are Biblical:
Believer (at least 20 New Testament passages, many more individual verses)
Saint (more than 25 passages, beyond the greetings and closings of Paul's letters).
Disciple (27 times in Acts, including Acts 11:26 which tells us that the disciples were first called Christians in Antioch. Also references in the four gospels, including in the Great Commission in Matthew 28:18-20).