Where did we get the idea that we shouldn't have to suffer? We get upset with God when we ask Him to take us out of a painful situation, but He doesn't. We can see no good coming from having to suffer.
If you are suffering, and have asked for God to heal or deliver you - but He doesn't, don't find it strange. The Bible tells us that Jesus learned obedience through the things that He suffered (Hebrews 5:8 - "Although He was a son, He learned obedience through the things which He suffered.") ("He had to be made like His brethren in all things so that He might become a merciful and faithful high priest.... For since He Himself was tempted in that which He has suffered, He is able to come to the aid of those who are tempted." ). In order to intercede for us, and be able to comfort us, He had to suffer the same things we suffer. And this is what we also do on this earth. We are to be "little Christs" (the Greek word for Christian means little Christ), ( Hebrews 2:17, 18; "He has made us to be a kingdom, priests to His God and Father" Rev. 1:6); If we can't relate to suffering of all kinds, then we cannot do what God tells us: "Blessed be the God and Father of our Lord, Jesus Christ, the Father of mercies, and God of all comfort, who comforts us in all our affliction so that we will be able to comfort those who are in any affliction with the comfort with which we ourselves are comforted by God." 2 Cor. 1:2-4. While we are here in this world, we are to represent God to all people and our lives should be a testament of who He is. We cannot do that unless people see us go through painful things and still have faith in Him, still loving Him.
You will suffer in this world as a Believer, or a non-Believer. But there is purpose in the Believer's suffering.