There are a few sources that estimate the wealth of very rich people, such as the Guide to Private Fortunes and Who's Wealthy in America. You can often find these directories in the Foundation Center libraries (see "Foundations") and in the libraries of large nonprofit organizations.
In addition, newspapers and magazine articles sometimes estimate a person's wealth, and some run lists of the world's wealthiest people, most notably Forbes (see Forbes' World Billionaires and the Forbes 400 Richest People in America). See also the Bloomberg Billionaires Index of the 20 wealthiest people in the world.
In some circumstances you can buy a person's credit report, which generally includes useful information (see "Credit Reports"). If you are calling from a law firm, insurance company or government agency then can try contacting companies such as CheckMate Strategic Group, Lutz Asset Research (212-760-0242) and the Worldwide Intelligence Network.
To locate bank accounts, brokerage accounts, mutual funds, etc. see "Collecting and Enforcing Judgments."
Other than that, there is no good or easy way to determine an individual's wealth. Some useful entries in this Guide that might help you identify a person's assets and liabilities include "Compensation," "Liens," "Real Estate," "Shareholders," etc.
Accurint, KnowX.com and Lexis would all be useful database vendors for locating assets and liabilities. Also check for lawsuits, UCCs and other liens, judgments and bankruptcies; some of the filings might indicate assets and liabilities. I haven't used them, but Investigative Consultants, Inc (ICI) claims to have global data.
Ultimately, though, you will probably have to hire an outside investigator to determine an individual's wealth with any real certainty. Private investigator services include Kroll Associates, Pinkerton, the James Mintz Group, Financial Forensic Services, Inc and the Worldwide Intelligence Service. For more companies, see the ION Investigators Anywhere Referrral Service and/or the PI Magazine Directory.