Selfless, self-denial, dying to self
Matthew 4:2; Luke 4:2 - Jesus fasted for 40 days in the wilderness while being tempted by the devil.
On the assumption that fasting can be many forms of self-denial, not just not eating, we might add:
Luke 6:12 - Jesus prayed all night before selecting the twelve Apostles
Matt 6:16-18 - Sermon on the Mount. Fast secretly so that only God will know. NB Jesus said "When you fast" not "If". He assumes His followers will fast.
Matt 9:14-15; Mark 2:18-20; Luke 5:33-35 - Jesus questioned about why his disciples did not fast. They will but not while the Bridegroom is still with them.
Followers of Jesus
Acts 13:2 - While the church in Antioch was worshipping and fasting, the Holy Spirit told them to set apart Barnabas and Saul
Acts 13:3 - The church in Antioch prepared to send Barnabas and Saul out by fasting and praying (and commissioning them by the laying on of hands).
There are many references to fasting in the Old Testament. It was an established part of Jewish spirituality.
In Jesus' time
Luke 2:37 - Anna fasted.
The disciples of John the Baptist fasted (Matt 9:14-15; Mark 2:18-20; Luke 5:33-35).
The Pharisees fasted (Matt 9:14-15; Mark 2:18-20; Luke 5:33-35 as above)
Luke 18:12 - the prayer of the Pharisee in the temple.
There is only one reference to Jesus fasting from food (although that was a fast of 40 days and nights!) Given that it was a common practice and that Jesus intended His followers to fast, we can probably assume that Jesus fasted on many other occasions.
There are, however, other ways to fast. Forgoing sleep so as to pray is a form of fasting.
Jesus' two referneces to fasting both assume that His followers will fast.