Can Christians be guilty of "robbing" God like it says in Malachi 3? God accuses the Israelites of "robbing" him by not tithing the full tenth according to the Levitical law. Can this also be true of believers today who are part of the new covenant and dead to the law?


  Malachi 3:8-11 ESV Will man rob God? Yet you are robbing me. But you say, ‘How have we robbed you?’ In your tithes and contributions. You are cursed with a curse, for you are robbing me, the whole nation of you. Bring the full tithe into the storehouse, that there may be food in my house. And thereby put me to the test, says the Lord of hosts, if I will not open the windows of heaven for you and pour down for you a blessing until there is no more need. I will rebuke the devourer for you, so that it will not destroy the fruits of your soil, and your vine in the field shall not fail to bear, says the Lord of hosts.


The reason I ask is because this is one of the go-to passages people use to encourage tithing because of the benefits that come from it (God will pour down a blessing). If that's the case, then are the downsides of not tithing shown through this passage also true?
The New Testament is silent on the topic of Tithing. This left us with our own interpretation of the Old Testament laws regarding Tithe. Most of the Pentecostal and Evangelical denominations make it an obligation to Tithe while the Catholic church doesn't collect Tithes. 

If we study the life of the first century Christians, they did not pay Tithes but instead, they sold everything they had and put it at the feet of the Apostles. They did not give 10%, they gave 100%.


  All the believers were one in heart and mind. No one claimed that any
  of their possessions was their own, but they shared everything they
  had. With great power the apostles continued to testify to the
  resurrection of the Lord Jesus. And God’s grace was so powerfully at
  work in them all that there were no needy persons among them. For from
  time to time those who owned land or houses sold them, brought the
  money from the sales and put it at the apostles’ feet, and it was
  distributed to anyone who had need. (Act 4:32-35, NIV)


The NT simply say that you should give to God whatever you are willing and give it with a cheerful heart. But do not try to lie about the money to the church as Ananias and Sapphira did. 

To answer the question, it actually depends on how you interpret the OT laws. Some take this verse from Malachi literally and pronounce blessings and curses. But the NT is silent on this. Remember that many laws from OT are now obsolete but it is not clear whether Tithing is obsolete or not. Nevertheless, the NT gives emphasis on giving to God and His servants. 


  Nevertheless, the one who receives instruction in the word should
  share all good things with their instructor. (Galatians 6:6, NIV)


So, give as much as you can. For the more you give, the more you will get. The less you give, the less you get. Don't just give 10%. Give 20%,30% or even 100% and God will bless you as He promised in Malachi. But I don't know about the curses.


  Remember this: Whoever sows sparingly will also reap sparingly, and
  whoever sows generously will also reap generously. Each of you
  should give what you have decided in your heart to give, not
  reluctantly or under compulsion, for God loves a cheerful giver.
  And God is able to bless you abundantly, so that in all things at all
  times, having all that you need, you will abound in every good work.
  (2 Corinthians 9:6-8, NIV)