Charismatics do a lot of 'binding and loosing', but the general charismatic understanding of these terms is not really based on scripture so much as it is assumption.
First of all, the context in which the teaching "whatever you bind in on earth..." is given is matthew 16 and matthew 18, both of which specifically deal with the authority that Jesus gave to the apostles over the Church.
In Matthew 16 it is directly connected to Jesus giving Peter the "keys of the kingdom". In biblical symbolism (indeed in most ancient symbolism) keys are a symbol of authority because the one who has the keys controls, he is the one who is rightfully in charge and he can allow people entrance or refuse them entrance.
In Matthew 18 the context is almost exactly the same except that it is directed at all of the 12 apostles and not specifically at Peter.
Further context from Jewish culture and religion is that the terms binding and loosing were commonly used in Jewish religious law for the authority to forbid, or allow an action or a practice. Essentially it was the authority of a Rabbi to say this practice is allowed for the people (loosed) or this practice is forbidden for the people (bound).
Given this realization, what Jesus says about binding and loosing has nothing at all to do with binding spirits, or loosing blessings on people and all that. This is simply what modern people have imagined it to mean.
Consider how charismatic people today use these terms and the ideas they have about them... do you see them being used that way anywhere in the New Testament? The answer is no, you will not find it there. It is highly unlikely that Jesus would give out this authority to bind and loose and then no one including the apostles ever used it.... thus the fact that it never appears in the New Testament as modern charismatics use it, probably means they are misunderstanding it.
What binding and loosing is actually about is the authority that Jesus gave the apostles to establish the practices and observances of the Church. The way of worship, etc. It is also related to the authority that Jesus gave the apostles to discipline the Church up to and including the authority to allow people in or to cast them out.
Now, the improper understanding and misuse of "binding and loosing" doesn't mean that Christians have no authority over spirits or that they can't bless people etc. It does, however, tend to change the way that authority is used, and maybe viewed.
When people are 'binding and loosing' they tend to get focused on themselves and start trying to operate out of their own authority. You can see this in the tone they take and the language they use.
The biblical model is submission first to God, and then resisting the devil from a place of submission to God. In this there is always the recognition that it is God that is really doing the work.
As Jude reports, even the Archangel Michael did not rail against Satan, but said only "The Lord rebuke you".
There is no need to go around ordering things to be bound, or to 'take authority' (which in fact is impossible, authority can only be given... to take authority is by definition usurpation). We simply need to submit to God, and resist the devil.
When the apostles had a hard time casting out demons, did Jesus tell them "well first you have to take authority, then you bind the demon, then you order it out..." I'm sure you're all aware this is not what Jesus told the apostles.
What he told them was the demon they were dealing with only comes out by prayer and fasting. This doesn't mean they needed to fast while they were trying to cast out the demon.
What Jesus was telling them was that they needed to have already spent time in prayer and fasting before hand. Why? because then they would have been in a proper place of submission to God.
