I want to make 8-bit art for a game.

I think the NES has 32 colors. 16 for sprites, and 16 for background.

You can use the MMF editor or any other art program. Just make a quick color palette and stick to it for the entire frame. You can switch palette on different frames, just don't exceed 32 colors.

EDIT:
But that's the NES. Read this here:
Please login to see this link.

Don't use more than 256 different colors. You can set your application to 256 color mode.

You can use Photoshop with PENCIL tool. It has rough drawing with cursor and as LB and willy said, you need to choose a palette then.
Look around for pixel art tutorials and you can get a good start from.

And since when was Photoshop FREE?

I already posted this in the other thread, but if you just want to do pixelart, then "Pixelformer" is a really nice little app, and a huge improvement over MMF2's built-in image editor or MS Paint.
Please login to see this link.

"The Gimp" and "Graphics Gale" are the other main free alternatives, but I personally don't like either of them.

To clarify, are you looking to make "8-bit game" art or simply "8-bit art"? The former being an for 8-bit console and the latter being art that is limited to 256 colors.

In either case, making pixel art is simple with any tool that allows you to paint a single pixel (usually the pencil tool in graphics programs). But I wouldn't say it is "easy" to make pixel art unless you have a good amount of art skill and understand the basics of making pixel art from a design standpoint.