Self-denial is an important part of the Christian life. Jesus sacrificed His life for us and He demands that we die to ourselves that we might experience the new life He has provided.  We do this by realizing that we can't save ourselves by our own effort and, by trusting God - not self - for salvation.  Then daily, we need to deny our own wisdom and seek God's wisdom and direction for our lives.

Self-denial is only good when we are denying ourselves for the purpose of exalting Jesus and His will for us in some area of our life.  Some have made a religion out of self-denial and find pleasure in their denial - not in Jesus' lordship.  This leads to legalism and bondage, which Paul condemned as will worship (Colossians 2:23). We are told not only to deny ourselves, but to "deny ourselves, take up our cross, and follow Jesus."

The cross is what Jesus died on.  There are circumstances in our lives which, like the cross of Jesus, give us the opportunity to die to ourselves each day. These are not things like sickness, poverty, etc.; Jesus' atonement provided redemption, but rather things like persecution (which we are not redeemed from) and the constant battle between our flesh and our born again spirit.  The cross that we must bear is to take God's Word (which is His will) and put it above our own will in each situation every day.