For brokerage houses, there is an institution that is similar to FDIC - Securities Investor Protection Corporation (SIPC). SIPC protects an investor's assets in a broker at up to $500,000 (including up to $100,000 cash).
If your investment account has more than $500,000 a asset, it's best to spread that money at several different brokers. If your broker goes bankrupt and you have more than $500,000 with the broker, the SIPC would first cover your loss, then you will participate the liquidation of the broker's assets.
If you are making investments through an advisor, make sure your advisor only channel your money to a broker that participates the SIPC program. You can find if a broker is a SIPC member or not at SIPC.org.
Next, we will discuss if your money at the insurance company is safe or not.