The gift of tongues spoken of by the Apostle Paul in 1 Corinthians 12 is a special gift of the tongues. Not all members of the local assembly or Body of Christ have the gift of tongues.
1 Corinthians 12:10 (KJV) 10 To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues:
However, when one is baptized with the Holy Ghost (as a part of the salvation plan spoken by Jesus, Peter and Paul), the evidence of one filled with the Holy Ghost is speaking in tongues. In Acts chapter 1, the 120 in the upper room were baptized with the Holy Ghost and spoke with other tongues as it prophesied about in:
Isaiah 28:11 For with stammering lips and another tongue will he speak to this people.
Also in Acts 10, Cornelius' household received the Holy Ghost and spoke in tongues.
Note: When those that received the Holy Ghost and spoke in other tongues as the Spirit gave the utterance, they were no interpreters and many spoke in tongues in the upper room and in Cornelius' house all at once. However, Paul says that only 2-3 should speak in tongues and there should be an interpreter. If there is no interpreter than they should keep silent. This shows that the Apostle Paul was speaking about something different than the infilling of the Holy Ghost. He was speaking about the gift of speaking in tongues, like the gift of miracles and gift of prophesy and so on.
Check out this video about the baptism of the Holy Ghost.