Taking up our Cross to Follow Him

Matthew 10:38-39 is all about dying to ourselves.
"...anyone who does not take his cross and follow me is not worthy of me. Whoever finds his life will lose it, and whoever loses his life for my sake will find it."
Here losing one's life does not have to mean physical death. There are however, many faithful Christians who are martyred, and to ignore or deny this would tarnish their ultimate sacrifice for their faith in Jesus.
"There are more Christian martyrs today than there were in 100 AD...An estimated 164 000 will be martyred in 1999." - From 'Jesus Freaks' by DC Talk and The Voice of The Martyrs

As Christians we are to lose our life for Jesus' sake, that we might find life.
What does this mean if not dying?
Just before He takes up His cross and is crucified, Jesus was on the mount of olives. "He withdrew about a stone's throw beyond them, knelt down and prayed, "Father, if you are willing, take this cup from me; yet not my will, but yours be done." An angel from heaven appeared to him and strengthened him. And being in anguish, he prayed more earnestly, and his sweat was like drops of blood falling to the ground."
Here we see that even Jesus asked God for another way. He knew the suffering He was about to endure and didn't want to go through with it. Jesus even needed an Angel to offer Him support and strength. Yet He obeyed. Jesus willingly bent to the desires of The Father, He both figuratively and litterally layed down His own life for the glory of the Father.
'Taking up our Cross' to follow Him may mean (although it is unlikely in a Western nation) to literally die for our Faith as a whitness to Him. More often though it is laying aside our own desires, being willing to 'die' to our own plans and dreams, that He might be seen through our lives and His will be done, not our own.

It should not come as a surprise that this concept of dying to oneself or defeating our own will is not confined to Christian belief.
"It is a man's own mind, not his enemy or foe, that lures him to evil ways."
- Buddha
"I count him braver who overcomes his desires, than him who overcomes his enemies."
- Aristotle
"You should examine yourself daily. If you find faults, you should correct them. When you find none, you should try even harder."
- Israel Zangwill
What is confined to Christianity though is the power to overcome oneself, the power of surrender for the name and sake of Jesus.

That we might find life? We must die to ourselves and die to sin so that Jesus can reign in us and that we might have eternal life with Him. "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord." - Romans 6:23 Our own sinful nature can only earn us death, but eternal Life is not earned but given as a graceful gift from God. The Christians responce to Jesus' humble, and sacrificial, death for our sin must a humble, and sacrificial, death to our sin and indeed a death to our own desires.

Just as He layed down His life so that we might live, we must lay down our lives so the He might live in us.