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Illustrator is a standard in print graphics production, and is a useful skill for a freelance production artist. Its powerful tools may take a little time to learn.
One of its advantages is being resolution-independent. That allows artists to work in relatively small files (reducing computer crashes and wait times), but still be able to export them at large sizes and excellent resolution.
Illustrator is most valuable in print environments, so if your design focus is on the Web you may be able to get by without learning it. Still, it's a useful tool to add to your resume.