Answer:
It depends on which kind of banner you are talking about. A banner can be a web-based advertisement that sits at the top or side of a website (called a banner-ad) or it could be a printed vinyl banner like what I make at www.gobigbanners.com.
Web-based banners ads can be created in any photo editing software package (yes, even MS paint could do it) but you would first have to know the pixel dimensions that your ad needs to be.
Outdoor-durable full color printed vinyl banners can be created online at www.gobigbanners.com as I mentioned before. The graphic can be what you make online, or something you make in a photo editing package and upload to the site.
Hope that helped somewhat,
Eyezac