Reputable brokerages offer insurance. Just as the FDIC insures bank accounts, the Securities Investor Protection Corporation (SIPC) insures brokerage accounts up to $500,000 per account (including up to $100,000 in cash). Note, though, that this insures your account against your brokerage going under, not your stocks losing value. (Sorry!)
Many brokerages even surpass SIPC levels of insurance. There might be a shady brokerage or two out there that somehow isn't insured, though.
Ask your brokerage (or prospective brokerage) for clarification on what insurance protection it offers. The folks at the SIPC offer this advice:
"Those words [Member Securities Investor Protection Corporation] -- or 'Member SIPC' -- appear in all signs and ads of SIPC members. If you have a question as to whether or not a particular firm is a member of SIPC, you may call the SIPC Membership Department at 202-371-8300 or visit us on the Web at www.sipc.org."
Learn more about brokerages at our Broker Center -- where we help you compare brokerages and offer tips on how to find the one best suited to your particular needs. (The brokerage with the lowest commissions isn't necessarily the best one for you.)