"I went to a service in a local church and someone told me that if I didn't speak in tongues I wasn't really 'saved.' Does a Christian have to speak in tongues to be saved?"
For some time there has been a movement in some theological circles that implicates tongues as the mark of salvation. Although there are biblical texts that indicate tongues as a mark of the "baptism of the Holy Spirit" that came upon those who believe, it is not necessarily a mark of salvation.
The first mention of speaking in tongues is found in Mark 16:17. In this passage, a text considered by nearly all scholars to be non-marcan and extra-biblical, one of the marks of a believer is that they shall speak in "new tongues" (of course so is drinking poison and handling poisonous snakes). Most of the tongues movement, however, finds its support in the book of Acts and in the letters to the Corinthians. In Acts it is clear that speaking in tongues is one indicator among several of belief and right relationship with God (baptism, worship, communal sharing of property, prophesying, and serving are some of the other signs). According to Acts 1:5 Jesus told the apostles that they would be baptized with the Holy Spirit and not just water. On Pentecost, a feast day 50 days following Passover, the apostles were overwhelmed by the Holy Spirit and began to speak in other languages, though one should note, the languages they spoke were known languages. This event marks the "coming of the Spirit" to the church.
Later, in Acts 8, John and Peter to Samaria to visit the new Christians there. They placed their hands upon the new believers and prayed. The believers then received the Holy Spirit, and though what that meant isn't specifically indicated here, it is postulated by most this was speaking in tongues. In Acts 19 Paul visited the Ephesian believers. While he was there he asked them if they had received the Holy Spirit when they believed. They said no and Paul laid hands on them and they "received the Holy Spirit, they spoke in tongues, and prophesied" (19:6).
However, substantive as these cases are, they only indicate a minority of scriptural evidence about baptism, tongues, and salvation. In John 20:22, the resurrected Jesus came to the eleven in an upper room and "breathed on them, and said to them, 'Receive the Holy Spirit.'" However, there is no indication of any special manifestation of the Spirit on the apostles there in that upper room. Further, Christ claims that belief or faith is the primary indicator of a right-relationship (justification or righteousness) with God (Mark 1:15; Mark 16:16; John 3:16; John 6:29; John 14:1). Indeed, in Acts, even though Peter promised the "gift of the Holy Spirit" upon the new believers who heard his Pentecost sermon, there is no mention of any the 3,000 new believers speaking in tongues; a fact that would hardly have been overlooked by the author given the importance attributed to the miracle that day. Finally, in the whole of the book of Acts there are approximately ten acts of baptism recorded, and of these, less than half mention speaking in tongues as a mark of the Holy Spirit.
There is little doubt that speaking in tongues, either known or unknown, is one of the many gifts of the Holy Spirit, a fact substantiated throughout the Corinthian letters. However, scripture does not support the gift of tongues as being the sign of the Spirit, nor does it support the assertion that only those who speak in tongues shall be saved.