Recommending when to use and when not to use Illustrator involves a brief discussion about a couple of other programs in the Creative Suite: Photoshop and InDesign. Especially for new users, many of the tools and capabilities appear the same. They are, but there are both subtle and not-so-subtle differences between the programs that make differentiation necessary.
To explain this fully, let's talk about graphics first. There are two types of graphic formats: vector and bitmap. Vector graphics are created with curves and lines based on mathematical formulas. After you create a vector graphic, you can enlarge it, reduce it, or change it as much as necessary without having to worry about the graphic losing resolution.
Bitmap graphics, also called raster graphics, are resolution-dependent. The graphic itself is made up of individual pixels that hold color information about the graphic. When you work with bitmap images, you alter pixels, as opposed to manipulating lines and curves as you do with vector graphics. The most common use of bitmap graphics is in the form of digital photographs.
Although both Photoshop and Illustrator can work with either type of graphic, Illustrator is primarily a vector-graphic program. You can import bitmap images into Illustrator and work with them, but you have to be careful because what you see in Illustrator may not accurately reflect the graphic when it is output. In the same vein, Photoshop's true strength lies in the ability to manipulate bitmap graphics and images. You can work with vector graphics in Photoshop, but your tools and options are much greater in Illustrator.
As far as how Illustrator stacks up against InDesign, there are many similarities in the programs. However, it's all a matter of utilityyou need to look at what the programs were originally intended for. InDesign is a page layout program. It was created to help you design large documents with more than one page, particularly text-heavy documents. Although you can create vector objects in InDesign, you have more options for working with them in Illustrator.
Illustrator, for its part, does what the name says it does: creates illustrations. It does have some page layout and text features, and it might be suitable for creating simple, one-page documents. But for the most control over document functions, look to InDesign.
The great thing about all these similarities, and even the differences, is that with the entire Creative Suite, you have access to all these tools and more. In addition, because the three programs work so well together, you end up with a tightly integrated workflow that can help you create better documents than you thought possible.