Must we speak in tongues in order to be saved?

No, you do not have to speak in tongues in order to be saved. Unfortunately, there are groups, usually the Oneness Churches who teach that you must speak in tongues in order to be saved. Additionally, they maintain that speaking in tongues is a necessary sign of the indwelling of the Holy Spirit because in the book of Acts, after the Holy Spirit moves on people they speak in tongues.

The problem with this position is that it fails to incorporate the biblical teachings that the Holy Spirit gives different gifts to different people in the Church.

1 Cor. 12:7-11,28-31, "But to each one is given the manifestation of the Spirit for the common good. ⁸ For to one is given the word of wisdom through the Spirit, and to another the word of knowledge according to the same Spirit; ⁹ to another faith by the same Spirit, and to another gifts of healing by the one Spirit, ¹⁰ and to another the effecting of miracles, and to another prophecy, and to another the distinguishing of spirits, to another various kinds of tongues, and to another the interpretation of tongues. ¹¹ But one and the same Spirit works all these things, distributing to each one individually just as He wills...²⁸ And God has appointed in the church, first apostles, second prophets, third teachers, then miracles, then gifts of healings, helps, administrations, various kinds of tongues. ²⁹ All are not apostles, are they? All are not prophets, are they? All are not teachers, are they? All are not workers of miracles, are they? ³⁰ All do not have gifts of healings, do they? All do not speak with tongues, do they? All do not interpret, do they? ³¹ But earnestly desire the greater gifts.

As you can see, not all have gifts of healings, or tongues.  Clearly, the Bible teaches that all do not speak in tongues, not because they can't, but because they are not gifted to do so.  Therefore, the idea that someone must speak in tongues to be saved is incorrect.