Here's the material breakdown:
Glass, metal, ceramic, and hard ABS plastic are inert and can be kept with anything without causing damage (though glass can chip if not protected by cloth or padding, and very heavy toys shouldn't go directly on top of squishier ones). I'm pretty sure the same goes for wood, but don't quote me on that since I'm not sure if the finish would cause reactions in other toys.
Pure silicone toys can be kept together. Some people feel safer keeping silicone toys from touching, or only keeping silicone of the same brand together, but if it's truly 100% silicone then it shouldn't be a problem (I myself keep my pure silicone dildos, from several different companies, all together, and there hasn't been a problem). Be careful, though - some toys labeled as silicone are actually silicone mixes (such as TPR silicone) and these should be stored separately. Eden's pretty good with getting accurate material information most of the time, but if you're uncertain then it's best to play it safe.
Most other materials should be stored on their own to avoid having them damage one another.