1 Peter was delivered through the prayers of people that weren't really expecting those prayers to be answered. In fact, they were surprised that their corporate prayer actually yielded results (see Acts 12:1-16).
2 Paul had faith in the power of corporate prayer. Paul believed that God would change the course of his life through the prayers of fellow believers (See Philemon 1:22; Romans 15:30-31) .
3 Jesus said that when we agree together we can ask according to His Name (i.e. His Nature, Character and Authority - see Matthew 18:19-20) and it will be granted.
Corporate prayer according to the good, perfect, or acceptable will of God (Romans 12:2) changes things. When we pray in symphony as a group of believers we pray the will of our Father in heaven to be performed on earth. He hears our effectual fervent prayers (James 5:16) and answers them - sometimes to our surprise!
When believers pray together according to the will of God - miracles happen!