If it shows up in the font menu for InDesign, it will show up in the font menu for Illustrator, assuming both programs are of reasonably similar vintage AND on the same computer...

Right... unless the font file is located in a private InDesign location, such as a "fonts" folder in the InDesign app folder.

For me, the situation described by Thomas applies only to the fonts Kenten Generic and Adobe Sans MM (I have the CS3 suite).

In fact, I can't even select those two fonts in inDesign though they are in the Required/Fonts folder of the application. So, I guess that all the fonts I can see in inDesign are installed systemwise.

Yes—but some folks use the private InDesign fonts folder as a sort of font management shortcut. Older versions of the app installed fonts there, also.

(And apologies for the post duplication above. Got fooled by TypeKit's lengthy lag after hitting post....)

T