I use Illustrator extensively for charts and graphs (try doing that in Photoshop!) and for logos and other spot art. Because the art is vector, not rasterized, there is no halo when the art is placed on a background, and the edges are always smooth.
In Photoshop, you need to consider resolution -- big files for full page ads, small files for business cards -- but in Illustrator, it fills the space at the time of output to match the size and printer (the difference between Vector and Rasterized art files). So you don't need multiple files because of different resolutions, though adjusting line weight might be a reason to have a couple of size versions.
Changing color is a simpler: there is no anti-aliasing to interfere with color selection, so you can build a rainbow of logos easily. On the other hand, you can't colorize from within Quark or other host applications the way you can with a Tiff format.
Illustrator takes less memory, because the computer doesn't have to remember on a pixel-by-pixel basis. This can turn into big time-savings.
You can draw in basic shapes very quickly, and combine or cut out overlaps. Once you have the shapes, you can port them over to Photoshop for embellishment. It's a lot easier mocking up a package in Illustrator than in Photoshop, for example, and it can dropped into a photo, then be distorted into perspective and tweaked for lighting and colors to make it look natural.
Some illustrators do a lot of their layout work in Illustrator, where they can nudge control points and other features, then bring them over to Photoshop for all kinds of filters, speckling, airbrushing, and other "personal touch" elements. Bert Monroy, for example, has written a book or two about his photo-realistic techniques, and how he combines the two programs.
Just a few reasons why you might want both.
