OK, before i really get into a game (or finish learning basics) i was wondering if drawing my own art on a piece of paper then scanning it is a good way to do art for games?

That entirely depends on what kind of game you want to make. There are plenty of 2D games that use hand-drawn assets, some that try to look hand-drawn and others that are just very cleanly rendered.

Anything requiring animated art assets will likely need to be additionally edited/compiled in a pixel- or vector-based graphics program like gimp, Photoshop, Illustrator, Flash, etc.

3D assets will always need a software program to create.

for now i'm just making simple pong for my first game (then add like boots and stuff)
then maybe a sidescroller

Then yes, you could easily use scanned drawings. A static image of a paddle or ball can be moved around by the program itself, so you wouldn't need to draw animation frames or anything that detailed.

You still likely will want to clean up and crop the scans though, there's a thread stickied at the top of this forum called "Free 2d/3d art assets '09!", I suggest looking there if you don't have a preferred tool already.

Good luck!

It's almost always going to start that way. (unless your using a tablet)
But once it's scanned you'll need to take it into Photoshop, Illustrator, or similar program and convert it to a usable asset.
I've used plenty of hand drawn textures in my 3d work. Hand drawn concepts are almost always the begin of the pipeline though so keep drawing. :)