There's been plenty of surveys on the question - and some conflicting results. Part of the reason the numbers change so much is that it's not always clear whether all debts are included, just 'problematic' debts or in sometimes only unsecured debt.
If there's no further qualifications, most Americans are in debt. Bearing in mind that things like mortgages and car loans count; it's the American dream for most to acquire a big debt of their own. In fact, according to the Washington Times, home-mortgage debt has doubled to $8 trillion since 1998.
Home and auto loans aside, most American's have credit cards. While about half of us do a pretty good job of keeping our balances down, the other half carries at least a $1000 balance, with 10% of card holders carrying in excess of $10,000 on plastic alone. Even those who carry only a few hundred bucks at a time are technically "in debt" - just an amount of it they can manage reasonably.
Some studies don't include what we'll call 'intentional' debt such as mortgages, and focus on things like credit cards and other bills that have unintentionally accumulated balances. If that's the case there are fewer Americans in debt, recent studies show about 45% of homes carry at least some balance on their cards rather than pay them off each month.
So how many Americans are in debt? Excluding minors, the total is somewhere in the neighborhood of 80% if we include secured debts like homes and cars. Excluding those particular purchases puts us closer to 50% of the adult population, and half of that 50% has thousands of dollars owed.