How do I check the 'health' of my brokerage?

How can I find out the health of my investment brokerage (like Fidelity.com, E-Trade, etc)? Can brokerages even crash and lose my money like in a bank failure? Much public focus has been placed on having a bank fail and people not getting their money. I know that in the case of banks, the money is covered up to 100,000 of FDIC coverage and there are sites to look up the health of your bank like http://www.bauerfinancial.com which give banks star ratings based on their current financial stability. However, what if you have your money in stocks/mutual funds in a place like Fidelity.com or E-Trade? Can these places fail and not be able to pay you back? Are there places that rate how safe/healthy these institutions are?