Pixel art software: The best programs
There are many different graphic software packages available which you can download online. Most aren't perfectly suited towards creating pixel art, but some work quite well. These are my personal opinions... if you want colorful graphs & flow charts listing the differences you'll have to go somewhere else online.
The big daddy of all art software is Photoshop. Is photoshop good for pixel art? Yes, sometimes. However - you have to be careful with what you do with it. Pixel art needs certain things, like blurring and anti-aliasing, to not be done by default with your brushes. The pencil tool is usually recommended. The cheaper Photoshop Elements, and it's sister Corel Draw series are not all that great for drawing sprites. These do come bundled with wacom tablets (great tools for drawing!) and other accessories though.
Not all programs have to be that expensive. Graphics Gale is generally free to use (the "lite" version is good enough for almost everything pixel-art wise). It also contains onion skinning, which is great for doing animations as it lets you draw overlapping the previous frame as a blueprint. The Gimp and MS Paint (yes, it's good for something!) are both free pixel art software that are highly recommended in drawing communities, but I haven't had good luck them.
Another choice is Pro Motion. This software was used by animators and pixel artists at professional studios. It's not cheap though, so take a look at it's webpage first to see if it's right for you.