Mike,
ALT 0176 will give you ° the degree symbol which is an extended character in most of the standard font sets. To see all characters, including extended characters in any particular font, use Windows Character Map (charmap.exe) which you'll find in Programs\Accessories\System Tools\Character Map. You might wish to make that into a Shortcut (just drag the exe file onto your Start button or Quick Launch area of Task Bar, which makes it quickly available to you. Put the font into the fontname box and click on the character/symbol and you'll see it's code in the lower right box of the menu, or you can do a Copy/Paste, but be sure you have selected THAT font in Illustrator with it's insertion point or you may get something else entirely. Some fonts even use a different code, but generally they are the same for things like accents and typical symbols like © (ALT 0169) or ¶ (ALT 0162). You MUST use the numeric keyboard with NumLock set in order to use CharMap. Keyboard numbers will not work.
Bob