Over the years I have heard various opinions about single missionaries that range from "I'll never agree to send single missionaries again" to "We should leave all missions work to singles." I don't know where you fall on this spectrum, and that may be why you are puzzling over this question: what role could a single person have in missions?
I don't think I need to cite much in the way of Biblical proof or the history of missions to establish the fact that singles have done great work in the past. The apostle Paul, Adoniram Judson, Hudson Taylor, Mary Slessor, Glady Aylward, and many others all went to the field single. Some married during their time there, and others didn't. In fact, Paul argues in 1 Cor 7 that it is better to be single in any case, and especially in ministry.
As singles go to the mission field, they may be called on to do a full range of ministry: teaching children, teaching marriage classes, counseling married couples, instructing people much older than they are, and even holding leadership positions such as pastor or elder (as Paul did). As in the case of married people, gifts for service come from the Holy Spirit and power, wisdom, and any other equipping comes from God too.
Since singles usually have no children or other dependents, they can be free from certain responsibilities to travel widely, be flexible with their time, and use less money than married people. Obviously, in the history of missions, married people have been called on to do all of these things--and even more--but these would likely cause less stress on a single person.
Churches often have a larger number of women than men, and women statistically speaking seek counseling more often than men, so it is wise for a church to have a larger number of Women Bible teachers and Women counselors than Men. Single women can help fill this gap. What exacerbates this problem is that often married women devote a large amount of their time to help their husbands' ministries and their children so that they have less available time to devote to church work than the single women. Again, single women can help fill this need.
In some societies where the Bible is not considered the standard for behavior and relationships, singles may be looked down on and given undue pressure to marry. A single church worker can be a role model to the Christian singles in that area to rejoice in the status that God has blessed them with and to serve God in ways best suited to them. With the high rate of divorce in many countries, a single church worker can be an example to people recently divorced as they learn to rely on the Lord as singles facing the future without a spouse but in the fellowship of the church.
Like married missionaries, a single missionary is wise to team up with other missionaries--whether single or married--for fellowship, encouragement, and full interaction in the church. Singles should keep in touch with their families and key friends for their social well-being, and should keep in mind the special vulnerabilities their status brings.
Can singles have a great ministry? Definitely! Much of the missionary work throughout the history of the church has been borne by singles, and the efforts of their lives of ministry are still bearing fruit in our modern times.