Notifications that pop-out at the top right of the screen disappear after just a few seconds but you can change this time period via a secret setting. You can even make it so notifications essentially never disappear unless you click on them or otherwise dismiss them.
To change this setting, open a Terminal window (Applications > Utilities) and paste-in the following (this will set it so notifications stay on screen for half a minute; the number at the end is the number of seconds):
defaults write com.apple.notificationcenterui bannerTime 30
To have notifications stick around essentially forever, paste-in the following instead:
defaults write com.apple.notificationcenterui bannerTime 86400
Then log out and back in again for the changes to take effect. To restore the default time period, open a Terminal window and type the following:
defaults delete com.apple.notificationcenterui bannerTime