I think that the modern view of tithing is flawed personally. I do not believe that the old temple/tabernacle and levitical priesthood have been replaced by church buildings and paid clergy. I'll cover more on that later, but I think that alms is one of the main New Testament forms of giving.

If we look at Malachi 3:10 and consider that the storehouse may now be a heavenly ones, then alms would be the way to go if we are going to be "giving to God" with the intent of it ending up in His storehouse.