What kinds of things need to be included in a corporate style guide that can't already be found in S&W, AP, Chicago Style, etc?
I just finished working on a 150-page Corporate Style Guide, so while I can answer this question in great detail if you want, my answer is not for WritersSE, I think.
AP and Chicago are mostly about the construction of writing — when to use a semi-colon, how to capitalize, the placement of someone's title. A Corporate Style Guide, also called Corporate Standards, is much more about design. It covers fonts, colors, logos, graphics, branding, positioning of elements, and maybe specific phrases used by the company.
Of 150 pages, six cover wording, and there's only one grammar rule. Everything else is about how to create a document in InDesign or Quark or PowerPoint so that everything is "on brand."
UPDATE: Since you requested it, I'm grabbing information from several style guides:
Typography: font, size, leading, kerning, and space before for body text, heads, subheads, text after subheads, bulleted text and the bullets, footnotes, legal copy, disclaimers, pull quotes, page numbers, and company contact information.
Colors: Corporate colors, product-specific colors
Logos: Approved corporate logos, non-approved logos. How big the logo should be. Where the logo should be placed on the page. Partner logos and where they go in relation to the company logo.
Photos and Credits: If a photo of a writer is used, what size, color, and position. Type specs for bylines. If stock photos are being purchased, guidelines about what imagery is appropriate.
What paper can be used: General paper preferences and special paper used for certain pieces.
Table of Contents: font, size, leading, kerning, space before, tab stop, width of box
Charts: font, size, leading, kerning, and space before; approved colors and tints; visual examples; how to represent negative numbers; when to use percentages; how to handle footnotes
Layout: Examples of every conceivable kind of printed piece the company distributes, including stationery. Placement of logos, titles, text, margins, and page numbers are specified.
PowerPoint: Everything in the previous sections, but for PowerPoint slides rather than printed piece.
Word: How to create stationery in Word. Position of the logo, fonts to use, margins, what information goes in the footer.
Emails: Font and size. Instructions about subject line, who to CC, and the signature block to append.
The phone: The exact wording of what to say on your voicemail, and what to say if you are on vacation. How to answer the phone.
Wording: Special phrases the company uses. Grammar quirks. When to use the serial comma. Spelling out numbers. How to format certain phrases in body copy. How to format phone numbers and times of day. How a press release is structured and worded.
As another example, you can look at the Apple Publications Style Guide (2009 version; 224 page PDF).
It includes information such as:
Basically, it contains a little of everything from general English usage to specific information about products. If you write about tech, it's a very handy resource to keep around.