There are several start-up warnings that your Mac can present, which indicate something is wrong with your system. If the boot chimes are replaced by any alternative audio signals such as loud beeps, then this indicates the system's hardware or firmware is malfunctioning or not properly set up. Provided the system's hardware is working properly, then you may see a blinking question mark if a boot volume cannot be found, but beyond this you may see a prohibitory sign show up on the screen.
Generally when the prohibitory sign shows up, you will initially see the gray Apple logo, followed by the presentation of the prohibitory sign after a few moments. This indicates that the system has found and recognizes your installed OS as a valid OS, but cannot boot from it because of some problem with the system. If this occurs, then there are two things you can do to fix it.
Boot to Safe Mode
Usually this problem happens because some kernel extension cannot be loaded or configured properly during bootup. If you have manually tampered with your system's extensions and have inadvertently edited one or changed permissions on it, then the system may not load it properly during start-up. If the extension is a nonessential extension, then booting into Safe Mode may allow you to fully boot the system, from which you can then try running permissions repair routines.
To do this, power down your system and then start it up with the Shift key held down, and if the system loads then open Disk Utility, select your boot volume, and then run a Permissions Fix routine on it. After the routine completes, restart the system and hope you can boot without the prohibitory sign. If you still get the sign, then download the latest "Combo" updater for your version of OS X from Apple's Support downloads site (http://support.apple.com/downloads), apply it when booted into Safe Mode, and then try restarting again.
As a final step, while rare this may also be caused by a faulty third-party application installation, so if you have recently updated or installed a new program and are experiencing this problem then you might be able to get around it by uninstalling the program. Again, boot to Safe Mode and either run the application's uninstaller or otherwise remove the program and its associated extensions (contact the developer for details on what files are associated with the program).
Reinstall OS X
If you cannot fix the problem by booting to Safe Mode then you will likely have to reinstall OS X. Luckily Apple makes this is a fairly straightforward task, especially with Snow Leopard where the default behavior for reinstalling will just overwrite the OS with a new installation, leaving your applications, data, and settings intact. Just boot off the OS X installation DVD and follow the onscreen instructions to reinstall the software.
If you are using Leopard, click the Options button in the installer and select the option to perform an "Archive and Install" method of installation along with checking the box to "Preserve Users and Network Settings." With this option you will likely need to reinstall some of your applications, but your data and settings should be as they were, and you should be able to now boot your system.