There is Biblical suffering which the Bible tells Christians to expect to have, and there is 'unbiblical' suffering which Christians are not supposed to go through. Below is something I've written on the topic. Although it was written more to address the issue of sickness, I'll just post it as it is:
Are you suffering for the wrong reasons?
If sicknesses and tragic accidents are not supposed to be part of a Christian's sufferings, then what things are? What, according to the Bible, are the types of sufferings Christians can expect to go through?
To answer the question, let us look at the example of Paul, followed by what Peter teaches about the sufferings of a Christian.
Paul's sufferings
What kinds of sufferings did Paul go through? Does he include sicknesses and accidents in his "list" of sufferings?
* 2 Corinthians 11:23-29
23 Are they ministers of Christ? (I speak as a fool) I am more; in labours more abundant, in stripes above measure, in prisons more frequent, in deaths [threats] oft.
24 Of the Jews five times received I forty stripes save one.
25 Thrice was I beaten with rods, once was I stoned, thrice I suffered shipwreck, a night and a day I have been in the deep;
26 In journeyings often, in perils [dangers] of waters, in perils of robbers, in perils by mine own countrymen, in perils by the heathen, in perils in the city, in perils in the wilderness, in perils in the sea, in perils among false brethren;
27 In weariness and painfulness, in watchings often, in hunger and thirst, in fastings often, in cold and nakedness.
28 Beside those things that are without, that which cometh upon me daily, the care of all the churches.
29 Who is weak, and I am not weak? who is offended, and I burn not?
* 2 Timothy 3:10-12
10 But thou hast fully known my doctrine, manner of life, purpose, faith, longsuffering, charity, patience,
11 Persecutions, afflictions, which came unto me at Antioch, at Iconium, at Lystra; what persecutions I endured: but out of them all the Lord delivered me.
12 Yea, and all that will live godly in Christ Jesus shall suffer persecution.
We can see that Paul's sufferings had to do with
persecutions and dangers, as he went from place to place preaching the gospel boldly. In fact, he makes in quite clear in 2 Timothy 3:12 that
all Christians who live godly lives in Christ Jesus will suffer "persecution". However, there is no mention of sicknesses or tragic accidents where lives and limbs were lost.
Even when Paul suffered shipwreck in Acts 27, it was because he was a prisoner forced to go on the voyage which he already knew would be disastrous (Acts 27:10). Even then, God delivered him as well as the entire ungodly crew to safety (Acts 27:44)! (See God delivers us out of them all!)
What Peter teaches
Peter also talks about the sufferings of a Christian. What types of sufferings is he talking about? Is sickness included? Why do Christians suffer?
Quoting from the NIV, you will see that
the sufferings of a Christian described in 1 Peter have nothing to do with sicknesses.
Sufferings: Unjust treatment and possibly beatings from harsh slave masters.
Reasons: For being God conscious and doing good.
* 1 Peter 2:18-23
18 Slaves, submit yourselves to your masters with all respect, not only to those who are good and considerate, but also to those who are harsh.
19 For it is commendable if a man bears up under the pain of unjust suffering because he is conscious of God.
20 But how is it to your credit if you receive a beating for doing wrong and endure it? But if you suffer for doing good and you endure it, this is commendable before God.
Sufferings: Insults. We also know that Christ was accused by false witnesses (Matthew 26:59-62); spat in the face, punched, slapped, ridiculed (Matthew 26:67,68); scourged (Matthew 27:26); stripped, mocked, spat upon, struck on the head with a reed (Matthew 27:28-31); and reviled (Matthew 27:39).
Reason: As an example for Christians to follow, that is, to humbly endure (not retaliate) persecution for being a good Christian.
* 1 Peter 2:21-23
21 To this you were called, because Christ suffered for you, leaving you an example, that you should follow in his steps.
22 "He committed no sin, and no deceit was found in his mouth."
23 When they hurled their insults at him, he did not retaliate; when he suffered, he made no threats. Instead, he entrusted himself to him who judges justly.
Sufferings: Harm and slander.
Reasons: For doing good and good behaviour in Christ.
* 1 Peter 3:13-17
13 Who is going to harm you if you are eager to do good?
14 But even if you should suffer for what is right, you are blessed. "Do not fear what they fear; do not be frightened."
15 But in your hearts set apart Christ as Lord. Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect,
16 keeping a clear conscience, so that those who speak maliciously against your good behavior in Christ may be ashamed of their slander.
17 It is better, if it is God's will, to suffer for doing good than for doing evil.
Sufferings: Bodily harm and heaps of abuse.
Reasons: For no longer participating in evil pagan activities but living for the will of God.
* 1 Peter 4:1-4
1 Therefore, since Christ suffered in his body, arm yourselves also with the same attitude, because he who has suffered in his body is done with sin.
2 As a result, he does not live the rest of his earthly life for evil human desires, but rather for the will of God.
3 For you have spent enough time in the past doing what pagans choose to do--living in debauchery, lust, drunkenness, orgies, carousing and detestable idolatry.
4 They think it strange that you do not plunge with them into the same flood of dissipation, and they heap abuse on you.
Sufferings: Those of Christ and insults.
Reasons: For bearing the name of Christ.
* 1 Peter 4:12-16
12 Dear friends, do not be surprised at the painful trial you are suffering, as though something strange were happening to you.
13 But rejoice that you participate in the sufferings of Christ, so that you may be overjoyed when his glory is revealed.
14 If you are insulted because of the name of Christ, you are blessed, for the Spirit of glory and of God rests on you.
15 If you suffer, it should not be as a murderer or thief or any other kind of criminal, or even as a meddler.
16 However, if you suffer as a Christian, do not be ashamed, but praise God that you bear that name.
Sufferings: Persecution, verbal abuse and false accusations.
Reasons: For righteousness sake and for Christ's sake.
* Matthew 5:10,11
10 Blessed are they which are persecuted for righteousness sake: for theirs is the kingdom of heaven.
11 Blessed are ye, when men shall revile you, and persecute you, and shall say all manner of evil against you falsely, for my sake.
God delivers us out of them all!
We have looked at Paul's sufferings as well as what Peter teaches about the sufferings of a Christian, and seen that they have nothing to do with sicknesses.
But what is important to note also, is that both Apostles say that Christ will deliver us out of whatever suffering we are going through!
Paul says:
* 2 Timothy 3:11
11 Persecutions, afflictions, which came unto me at Antioch, at Iconium, at Lystra; what persecutions I endured: but out of them all the Lord delivered me.
And although we may face the troubles that Paul faced, we must also ask ourselves if we are called to suffer the way Paul suffered, that is, to the same degree.
* Acts 9:16
16 For I will shew him how great things he must suffer for my name's sake.
Do all believers have this calling from the Lord? I don't believe God has this plan for every Christian. You might expect a Christian to have the same sufferings Paul had if he were called to preach the Gospel in, say, Afghanistan, but if he just goes to church on Sundays, I seriously doubt that he will suffer the way Paul did. (See also Was Paul's thorn some sort of sickness? and Trophimus left sick.)
In Peter's teaching on the sufferings of a Christian, he ends off by saying:
* 1 Peter 5:8-10
8 Be self-controlled and alert. Your enemy the devil prowls around like a roaring lion looking for someone to devour.
9 Resist him, standing firm in the faith, because you know that your brothers throughout the world are undergoing the same kind of sufferings.
10 And the God of all grace, who called you to his eternal glory in Christ, after you have suffered a little while, will himself restore you and make you strong, firm and steadfast.
Notice that he is telling us that these sufferings that Christians throughout the world experience are from the devil, not God. But the good news is this: the suffering is for "a little while", after which God will "restore you and make you strong, firm and steadfast"! In other words, these sufferings are not permanent and you are not supposed to die from it, unless you are called to martyrdom.
Below are more scriptures that show us that despite the persecutions and troubles we can expect to face, God will deliver us out of them all!
* Psalms 34:6
6 This poor man cried, and the LORD heard him, and saved him out of all his troubles.
* Psalms 34:19
19 Many are the afflictions of the righteous: but the LORD delivereth him out of them all.
* 2 Timothy 4:18
18 And the Lord shall deliver me from every evil work, and will preserve me unto his heavenly kingdom: to whom be glory for ever and ever. Amen.
So, even if you still insists that sicknesses must be part of a Christian's sufferings, then you must at least believe that God will deliver the Christian out of all sicknesses, to be consistent.
What about Job?
It is strange that Christians who believe in suffering sicknesses "for God's glory" often point to Job's sufferings, but never to his perseverance, healing, double blessings and long life.
They simply leave out the fact that Job's ordeal lasted only about nine months; that God finally healed job, blessed him with twice as much as he had before; and that Job lived to a ripe old age (Job 42:10-17).
This is certainly an inconsistent and lop-sided understanding of the book of Job.
Even James, when speaking of suffering, reminds us of Job's perseverance, and "what the Lord finally brought" about because "the Lord is full of compassion and mercy".
* James 5:11
11 As you know, we consider blessed those who have persevered. You have heard of Job's perseverance and have seen what the Lord finally brought about. The Lord is full of compassion and mercy. 
- not because they haven't any value, but because it's difficult to discuss the issue objectively when people become personally and emotionally involved in the debate.
