The best resolution wallpaper for your monitor will ideally match the resolution of your computer's screen. To find your screen's current resolution:
Windows Vista Users:
Right-click on your desktop and select "Personlize". Then click the "Display Settings" icon. This will bring you to your main display options, which will show you what resolution your monitor is currently set to. You may also change your monitor's resolution from here if required.
Windows XP Users:
Right-click on your desktop and select "Properties". This will open your main display options in a new window. In this new window, click the "Settings" tab, which will show you what resolution your monitor is currently set to. You may also change your monitor's resolution here if required.
Mac OS X Users:
Click on the apple logo in the top left of the screen. Select "System Preferences..." from the menu. Then click "Displays", under Hardware. This shows you the current resolution your monitor is set to and also allows you to change it if required.
Do keep in mind that in most cases it is also possible for your computer's Display Settings to "stretch" (a nice way of saying automatically resize) any wallpaper you choose. This function is usually set as your default option in your display settings.
Using this auto-resizing option works very well with wallpapers sized much larger than your working resolution. However, using this kind of function on a wallpaper smaller than your resolution will cause the image to lose quality and/or appear misproportioned.