It depends. You have to do some math.
For the sake of calculations, consider your screen as 800×600 pixels. If you expect your scanned image to fill the screen, you want it to be 800×600 pixels when scanned.
To get the DPI (or pixels-per-inch) number, do this for a horizontal image: widthxDPI=pixel width.
So:
A picture 8″ wide would have to be scanned at 100 DPI to give an image 800 pixels wide.
8″x100dpi=800 pix.
or 800/8=100dpi.
Now if you wanted to zoom into a 4×3 inch section of that picture, then you would want that 4×3 inch area to be 800×600 pixels:
800 pix/4″ = 200 dpi.
You see? Because you’re zooming in closer, you want more detail, so you have to scan at a higher dpi.
I’ll leave it up to you to figure out how to scan vertical shots and shots that are wider than 4×3. Just remember: it’s okay to go with a slightly higher DPI for good resolution, but if you go too high, you get a really big image that could slow down your work.