WASHINGTON—American taxpayers awoke Wednesday to learn they may end up owning one of the world’s largest insurers. They might now lose some sleep wondering whether the government’s $85 billion loan to American International Group Inc. was a wise investment.

If the gamble succeeds, the company nurses itself back to health, unhinged financial markets calm down and taxpayers turn a profit.

If it fails, the American public feels the hit—and possibly finds itself rescuing other major financial institutions, swelling the deficit and potentially driving up interest rates on mortgages, student loans and other debt.

Analysts said Wednesday the odds are pretty high that the rescue will be a good investment for taxpayers, with AIG paying off the loan at a relatively high interest rate and the government potentially making money off its nearly 80 percent equity stake in the company.

In 1979, the U.S. guaranteed $1.2 billion worth of loans to the struggling automaker Chrysler. When the company rebounded four years later, the government reaped more than $300 million in profits.

While relatively unknown on Main Street before Wednesday, AIG is a colossus on Wall Street and financial districts around the globe, with operations in more than 130 countries and $1 trillion in assets on its balance sheet.

Besides life, property and other insurance offerings, AIG provides asset-management services and airplane leases. Its myriad businesses are also linked to mutual funds, annuities and other retirement products held by millions of ordinary Americans.