Yes, I believe Jesus did have a sense of humor and made people smile (or even laugh) at some of the things He said. His purpose was serious, but sometimes He got His point across by making people see the ridiculous side of life.
For example, think for a moment about the image Jesus used to describe how hard it is for a proud, self-confident rich person to enter the Kingdom of God. He said it would be like a camel trying to go through the eye of a needle (see Luke 18:25). Can you imagine His audience not laughing as they tried to picture this in their minds? I can't. His point was serious -- but He used an exaggerated, humorous image to get it across.
Remember, too, what the Bible says about God's reaction to those who arrogantly decide they don't need God and are stronger than Him. They want nothing to do with God or with Christ, but God laughs at their pretensions and rebukes them for their sin. The Bible says, "The One enthroned in heaven laughs; the Lord scoffs at them" (Psalm 2:4).
Be grateful for your sense of humor, but don't use it to hurt or embarrass others, and don't overlook the tragedies and heartaches of our sin-filled world. Jesus wept over the failure of His people to repent and believe the Good News of God's love and forgiveness -- and so should we. Most of all, the Bible says, He was "a man of sorrows, and familiar with suffering" (Isaiah 53:3).