Sometimes Picasa seems to get in a loop and saves a screenshot every few seconds. The problem can be a defective keyboard or keyboard software. Things you can try:
Check to make sure the "PrintScreen" key on the keyboard isn't stuck
Try reinstalling the keyboard software
A 3rd-party tool such as RoboKey caused the problem for some users
As a final catch-all, you can do a really dirty hack: Revoke write permissions for yourself on the following folder at either of these two paths, depending on your version of Windows. This way Picasa cannot write to the folder anymore so it can't save any screenshots.
%USERPROFILE%\My Pictures\Picasa\Screen Captures
%USERPROFILE%\Pictures\Picasa\Screen Captures
Above paths did not work in Windows 10; try navigating to C:\Users\<YourUserName>\Pictures\Picasa\Screen Captures
Right-click Screen Captures folder > Properties . . . (search the Internet for exact steps after this!)