Why do we see in the OT God punishing people for doing evil, but we do not see or hear about God doing it today?

We can offer some thoughts on why this is, but please keep in mind that this is an opinion, of which there are probably many.  I am not aware of a "thus saith the Lord" which answers this question directly.

Throughout most of the Old Testament, God is dealing strictly with the nation of Israel as His chosen people (Deut 14:2, Psa 33:12, etc.)  The blessing given to Jacob by Isaac included a blessing for those who bless Jacob, and a curse for those who curse Jacob (Gen 27:29), and as such, God's actions in the OT are directly related to that nation.

The nation of Israel made a covenant with God at Sinai to obey Him (Ex 19:8).  When they were faithful to that covenant, God provided abundant blessings to them, starting with removing the natives from the land so that His people could inherit it.  The natives of the land worshipped false gods and YHWH punished them as a byproduct of blessing Israel.  When Israel was unfaithful to their covenant, God used the people of the land to punish Israel for their abominations.  When Israel repented, God blessed them once again, sometimes by punishing the very people He used to inflict punishment on Israel.  So most of God's actions in the OT were based on whether Israel was being faithful or not.

In the New Testament, Jesus opened a new and living way.  Instead of "I will bless those that bless you and curse those that curse you", the rule of love took over and Jesus teaches us to "bless those that curse you" (Matt 5:44).  The way that Jesus opened for those who entered into a covenant of sacrifice with Him (Psa 50:5, Rom 12:1), was the narrow way (Matt 7:14), the opportunity to run for the prize of the high calling (Phil 3:14) and become heirs with Him (Rom 8:17) as His bride and members of His body (1Cor 12:27, Rev 21:9).  This call is to individuals who believe in Jesus and are willing to make the covenant of sacrifice, and as such, the blessings and punishments from God are to the individual as chastenings from the Father (Heb 12:7). 

It is our belief that the blessings and punishments (chastisements) from God are just as prevalent today as they were in the Old Testament, but they are directed at the individuals who are in covenant relationship with him, rather than an entire nation.  Meanwhile, it appears that evil is running rampant in this world, and God is permitting it for a time in order to achieve His promises to Abraham, Isaac, and Jacob that "in the and thy seed shall ALL the families of the earth be blessed" (Gen 12:3, 26:24, 28:14).  This evil must come to pass in order to 1) test the prospective bride of Christ, and 2) bring about Armageddon (Rev 16:16) where the earthly evil systems are destroyed and God's Kingdom is built upon the ruins (Rev 21:1).