I grew up Southern Baptist, and a hallmark of Southern Baptist doctrine is believer's baptism. In brief, this doctrine argues that baptism is for those who have expressed their own faith in Jesus as Savior. It specifically excludes infant baptism on the grounds that infants have not yet expressed their own faith in Jesus. I still hold to believer's baptism, and here's one passage which I believe supports it. Acts 16:30-31 records Paul and Silas speaking with the Philippian jailer after their miraculous release from prison:
Then he brought them outside and asked, “Sirs, what must I do to be saved?” They replied, “Believe in the Lord Jesus and you will be saved, you and your household.”
Paul and Silas's response to the jailer is subject to two interpretations. It could be understood to mean that the faith of the jailer would automatically extend to his household. The imperative verb "Believe" is singular, directed only to the jailer, and the pronoun "you" in the statement is also singular. It appears that the only one who is called to faith is the jailer, but clearly his household is included. So this interpretation would argue against believer's baptism, as the household appears to receive the benefit of the jailer's faith without explicitly expressing that faith.
Against this, though, is an interesting rule of subject/verb agreement in Greek. Normally in Greek, as in English, a plural subject has a plural verb. Here, though, the subject is a compound plural ("you and your household") but the verbs are singular. In this kind of construction the emphasis is on the first named subject, so the verbs agree in number with that singular subject, but the second subject does the actions of the verbs as well. Paul and Silas used singular verbs to emphasize the Philippian jailer; he was the one standing right in front of them at the time. But they include his household, too, because they wanted the jailer to know that the good news about Jesus was available to them as well.
In short, Acts 16:31 supports believer's baptism because it shows that the jailer's household needed to have faith; if they did, then they would be saved, too.