Do Christians regard speaking in tongues as necessary? I have heard that some Christians consider it the only sure sign of having received the Holy Spirit, which would seem quite important. 

If not generally, which groups hold to this belief, and in what way do they consider it necessary? 

And secondly, does Christian tradition back up this belief? What evidence is there?
No, I do not believe that this is the only sure sign of the Holy Spirit.  Also, I would question if someone is truly speaking in tongues when they claim to be.  Can people speak in tongues today?  I have seen people who would claim they were speaking in tongues, but there was no one there to interpret.
Paul lists speaking in tongues as one of the spiritual gifts, but he does say that they are distributed as God determines, not necessarily as we want them.

1 Corinthians 12:7-11 (NIV)
7 Now to each one the manifestation of the Spirit is given for the
common good. 8 To one there is given through the Spirit a message of
wisdom, to another a message of knowledge by means of the same Spirit,
9 to another faith by the same Spirit, to another gifts of healing by
that one Spirit, 10 to another miraculous powers, to another prophecy,
to another distinguishing between spirits, to another speaking in
different kinds of tongues, and to still another the interpretation
of tongues. 11 All these are the work of one and the same Spirit, and he
distributes them to each one, just as he determines.
1 Corinthians 12:27-30 (NASB)
27 Now you are Christ’s body, and individually members of it. 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?