General:
* Corrosion
* Oxidation
* Red oxide
* Iron oxide
* Ferric oxide
* Scale
* Verdigris (for copper)
* Tarnish (for silver)
Figurative:
* Decay
* Deterioration
* Disintegration
* Erosion
* Wear and tear
The best word will depend on the specific situation. If you're talking about the chemical process, "oxidation" is a good choice. If you're describing the appearance of rust, "red oxide" or "scale" might be more appropriate. And if you're using rust metaphorically, "decay" or "erosion" could work.