Although it is never required, a banner can set the mood for a Web site and add
visual interest to an otherwise simple page. The possible variations are
unlimited and will be determined by the nature of your Web site, the mood you'd like to establish, your color scheme, and your personal tastes. Or you might decide to just use your company logo and the company name, without the textures, gradients, and other effects. It's entirely up to you!
Below are a very few examples of the possibilities.
This is the banner for the stoneArt by Twitchell Web site. The lettering uses a stone texture on a dark brown gradient, against a warm beige background. On the left and right, you can see the textured dark brown page background.
The Bit of Design Banner has an entirely different mood. It's a little more formal, includes a logo and some text about the company's experience and characteristics. Parts of the banner and the page background use matching patterns. The 'color-to-invisible' gradient allows the banner background texture to show through.
Of course, if you prefer simplicity, decorative graphic text against a light background can also be effective. Look at the top of this page for confirmation that I believe in simplicity (sometimes!)
Here are a couple of examples that both use the same background texture and the same colors. Only the text is really different, but that's enough to change the mood.
This one uses a very subtle background texture, a dark brown-to-transparent gradient, and another graphic text style that uses the background color and some enhancements.
An untextured background, old English lettering... a little more formal. The letters are filled with a 3-color gradient for a little extra interest. Whether it's appropriate or not will depend on the nature of your site, the mood you want to establish and, of course, your personal tastes.