When Apple introduced its "Natural" scrolling direction option in OS X to mimic the touch-based swiping on the iPhone and iPad, it also included a system preference setting to revert this, should you wish to use classic scrolling behavior. While this feature offers most users the choice to revert to a behavior they would prefer, it may not work in all situations, especially when using a mouse as an input device, instead of Apple's multi-touch trackpad.
In some cases, the setting might be available in the Mouse pane of System Preferences, but when you check it or when you close the system preferences, the setting reverts. At other times, the setting may simply not be present at all.
If the checkbox to revert scroll behavior is missing, then there may be a conflict between your mouse and the driver software being used in OS X. If you have installed the driver software that came with your mouse, then try updating it to the latest version from the manufacturer's Web site. The same applies to the use of third-party input management software and drivers, such as Better Touch Tool and USB Overdrive.
Alternatively you can try uninstalling the driver to see if using Apple's built-in drivers alone brings the scroll setting back.
If you are currently using only Apple's drivers and this setting is missing, then you might try the third-party drivers for your mouse, to see if they properly recognize its scrolling capabilities and give you settings to adjust them.
While adjusting your system's driver configuration in these ways may spur the system to give you the scroll direction setting again, an alternative that works just as well is to try forcing the system to invert the scrolling behavior.
One approach to this is to unplug all third-party mice and then use an Apple mouse with the system to hopefully reveal the setting, and then toggle it to your preferences. Then switch mice again to see if the setting maintains. The second approach is to use the OS X Terminal to set the scroll direction to your liking. This approach may also overcome problems where you have the setting in the system preferences, but it reverts or otherwise does not stick.
To do this, open Terminal, in the Applications > Utilities folder, and run the following command:
defaults write -g com.apple.swipescrolldirection -bool FALSE
To reverse this setting, repeat the command but use "TRUE" instead of "FALSE" as the final argument. Now check the setting by running the following command to read it back to you:
defaults read -g com.apple.swipescrolldirection
The output of this command should give you a 0 for false (which indicates classic scrolling), or a 1 for true (natural scrolling). After this setting has been changed, if the change does not take effect immediately, then log out and log back in to your account.
Sometimes because of preference caching behaviors in OS X Mavericks, some settings changes in programs, system preferences, or even those invoked by the "defaults" command in Terminal may not stick. If this is the case, when you use the second command above to read the setting, it may still show as reverting to the system default. If this occurs, then open Activity Monitor and search for the process called "cfprefsd."
There will likely be one such process running under the "root" account, and others running under the accounts of each logged-in user. Locate the one for your account, and then select and force-quit it. When done, try using Terminal to again invoke the settings change, and hopefully this time it will stick.