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Bitcoin is independent of the government & banking system
Bitcoin is an Open Source, Peer to Peer system which exists independent of any corporation, bank or government.
The only way that the Bitcoin protocol could be shut down is by shutting down the Internet. ISPs could, in theory, attempt to block Bitcoin traffic, but users would find ways to masquerade and hide Bitcoin traffic inside of other traffic such as web or email traffic.
While there is the Bitcoin Foundation, this non-profit can't exert control over bitcoin, and isn't able to shut bitcoin down or alter it in ways that would change its founding principles
A majority of Miners working in concert could change aspects of the Bitcoin protocol. This hasn't happened as of yet, and likely will only happen to make changes that would benefit all bitcoin users. Bitcoin miners are rewarded with Bitcoins for the mining they do, and hence they have incentive to keep Bitcoin as a stable, well functioning crypto-currency that is accessible and useful to all so that more and more people place their trust in and use bitcoin.
Several other derivatives of Bitcoin have been created (called AltCoins) which are competing for users/ market share based on improvements they've made to the bitcoin algorithms