Residency in Panama is very easy to obtain when compared to most other countries. There is even special legislation for 'pensioners', who can qualify for residency with a guaranteed pension income of $500 per month ($600 for a couple). You don't necessarily have to be an elderly person either, since anyone over 18 can qualify. However, it must be a pension from a recognized source: for example a government agency (e.g. Social Security, disability, armed forces, etc.) or if it is a company pension, it must be a defined-benefit pension.

Added March 2007 by Brian:
Regarding pensionista visa in Panama, I believe the law has changed that you must now be of pensionable age, not just 18+.
See http://www.lawyers-abogados.net/, specifically: http://www.lawyers-abogados.net/en/Services/Immigration/panama-pensioner-visa-change.htm

If you don't have a fixed pension, but you do have capital, you might consider investing in real estate. If you invest $200,000 or more in any kind of real estate, you can automatically receive an investor residency that allows you to live in Panama legally. There are other possible programs, such as "reforestation" and "small business investor", depending on your personal objectives once you are living in Panama.

While technically you may apply for the residency yourself, it is often wise to hire a lawyer specializing in these matters to make the application for you. You must hire a lawyer registered with the Panamanian bar association. A good lawyer will charge from $1000 to $1500 for the process.