The best way to not forget your tasks is by writing down small sticky notes on your computer screen. People usually use small stickers and paste them on their monitors.  Other guys use built-in stickies like we have it in Vista.

Unfortunately other major operating systems don't offer that but you can always use a third party application to get the job done. 

Stickies for Windows XP

Stickies for Windows allows you to put yellow sticky notes on your Windows desktop. It is simple, very customizable, and completely free. It offers tons of useful features that makes it quiet more interesting. It features

• Every aspect of the user interface is customizable, from the note colors and fonts to the icon in the system tray. You can customize every note on your desktop or change notes individually.
• Your notes and settings are saved automatically, so your sticky notes will remain on your desktop if you restart your computer or restart the program.
• Make sticky notes behave like normal windows, or you can make them remain 'floating' above all of the windows on your desktop so they are always visible.
• You can move notes by clicking and dragging anywhere on the note rather than clicking on the top of the window. You can double-click on the note to edit it.
• Stickies now supports multicomputer synchronization so you can have the same Stickies on all of your computers.

Unfortunately the official website is down but you can always use the alternative download link to get this app.

Stickies for Mac OS X

SketchBox is the perfect application for your Mac Desktop. It works as your sticky notes manager and allows you to not only enter text but also make drawings and set individual reminders for each sticky to use them as a visual alarm clock.

Unlike other applications it lets you arrange all your notes in thumbnail view and create short storyboards/comics or simply store your daily thoughts as searchable text.SketchBox is 100% free for you to use and if you feel like donating, you can do that by visiting their website.

Alternatively you can always use built-in sticky feature on your Mac.

Download Stickies for Mac

Stickies for Vista

Vista offers a built-in feature for stickies. To enable it simple use the Win + Space key combination to bring all of the gadgets to the foreground. You can then easily add gadgets to the sidebar by right-clicking anywhere on the sidebar or the system tray icon, and choosing Add Gadgets.

Your notes will sit in the Sidebar or you can drag them to the desktop where they will be larger and easier to read and edit if needed.

Stickies for Linux

Sticky Notes provides a way to have little sticky notes on your desktop. It supports different languages and it works great with Ubuntu Linux.  It is similar to knotes but does not require KDE.

Download Stickies for Linux

If I have missed anything, please use the comment box and let me know so that I can add it to the list.