Does Islam or Muslims believe in Jesus?

Yes, Islam teaches us that Prophet 'Isa (Jesus Christ) was a Messenger of Allah.

Allah says in the Holy Qur'an:

O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs.