According to Reformed theology, does God show special favor to some believers? I am looking for answer from a reformed theology perspective. I know that there are verses in the Bible that God does not show favor. But at the same time there has been many instances where the son was blessed because of the father. In some cases the children are cursed for sins of the father's when the children had not committed any wrong. Their family is put to death.

People quote that all our curses where nailed on the Cross so if we believe in Christ we will be free from these. But the reality in some cases doesn't confirm this. I see that some believers are chosen to suffer all the time for no fault while others in faith are shown favor most of the time. This is more discouraging when it's in the ministry and you don't have any results to show. 

It is not encouraging as a child of God, as this is like a human parents favorite child. A child has to learn to trust the Father but is not given a chance. The most common answer I get is you are not praying enough or probably in heaven you will be rewarded. Reality here is some how different from Theology and the question of a righteous God.
Friend:   Lets start in scripture:

First, Anything good that we have from God is by His grace, not because we can earn it.  Matthew 5:45 says “He causes His sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous.”  

God gives good gifts to all people, regardless of their righteous deeds.  Think about the “goods” you possess: life, sight, friendships, your relationship with God, water, food, etc.  Which of these things could you have possessed if God had not supplied them?  All good things are from God (James 1:17).  Nothing God gives us is earned. 

Paul was inflicted with a Thorn in his side,    Some of the Disciples suffered and were killed ...   

Romans 8:18 says “I consider that our present sufferings are not worth comparing with the glory that will be revealed in us.”  But sadly, people pass up eternal blessings because of their focus on the temporal.

The blessings some believers have vs others is not what God wants us to focus on. 

In fact - All Things Come to the Good of those who Love the LORD and are called according to HIS purpose. 

If His purpose is for you to suffer like Paul did with a thorn in his side - so be it. 

If His purpose is for you to have more wealth than anyone can imagine - so be it. 

The Key is - what is His Purpose? 

Rev. 4:11 says, "You are worthy, our Lord and God, to receive glory and honor and power, for you created all things, and by your will they were created and have their being."

You might find comfort in knowing you are not the first to wonder about this... 

Centuries ago the prophet Habakkuk complained to God, “Why do you tolerate wrongdoing? … Why are you silent while the wicked swallow up those more righteous than themselves?” (Habakkuk 1:3, 13).

Perhaps we really need to examine what a blessing is:

Is it riches?
Is it tons of people in the pews if you're a pastor? 
? ? ?

Jesus said, “Blessed are those who hunger and thirst for righteousness, for they will be filled” (Matthew 5:6).

Perhaps the Greatest Blessing my friend is simply Knowing Christ and resting in the Eternal Promise that his Grace is Sufficient to be the propitiation for our sins. 

There is Nothing in scripture - when Read in full context that states that we as Christians are going to live a full Life abundant and free from persecution, from hardship and trials. . .  Nothing. 

Sadly - there are those who teach this "prosperity gospel" stating God wants you to be Rich and its a sign of Gods blessing on your life. 

I call fiddlesticks:

Galations 3:14 is often used by folks to show God wants you to be rich and reference the "blessings of Abraham" . . .  of course they only use the first 1/2 of the verse.   If we examine the second half we read  “that we might receive the promise of the Spirit through faith.” Paul is clearly reminding the Galatians of the spiritual blessing of salvation, not the material blessing of wealth.

Using Paul again - we can jump over to 2 Corinthians 8:9, “For you know the grace of our Lord Jesus Christ, that though he was rich, yet for your sakes he became poor, that you through his poverty might become rich.” 

Sounds awesome right -    FOR YOUR SAKE he became poor so you might become rich...   

How awesome -   until you read the text in its entirety.  Paul was teachign that since Christ did so much by being the propitiation for our sins - the Sacrificial lamb that each should empty themselves of their riches in Service to the King of Kings and Lord of Lords -    just 5 verses later we see where Paul was urging the Corinthians to give their wealth away to their needy brothers, writing “that now at this time your abundance may supply their lack” (2 Cor. 8:14).

God's blessings have nothing to do with money, fame etc. . . 

The blessing of Eternal Life in Service to the Father is the true reward.