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The short story: Use PDF, .ai, .psd, or .tif for graphics to be printed (although you can get away with .jpg files on your small desktop printer). Scan images as TIFFs. You can actually place another InDesign file onto an InDesign page.
Avoid PICT, WMF, BMP, PNG, and only use EPS and DCS if you know what you’re doing and have no choice.
When saving an .ai file in Illustrator, make sure the box is checked to “Create PDF Compatible File” in the options when you save the file or InDesign won’t be able to read it. Avoid EPS files, if you can, only because they are an old technology and not as dependable as .ai files.