What is the Shari'a rule about using bank accounts with interest for a Muslim living in the West? Can I take the interest and give it to Islamic causes or should I leave it in the bank?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Depositing money in usury-taking banks is not permissible. If one fears for his money than he must deposit one's money in the banks that act according to Islamic Shari'a. If such banks are not available then, based on the rule necessities have no laws, one may deposit his money in a current account that does not gain usury/interest in usury-taking banks.
If one cannot do so and has deposited money in a saving account, he should get rid of the interest earned since it is hateful money. So, it should not be used for oneself and for his family members. If one leaves the interest for the bank it will give it to Jewish or Christian organizations that will use it in evil purposes, so one should not leave that money to the bank. Instead it should be spent on needy Muslims, to be given charity organizations, Islamic schools and in good projects.
Allah knows best.