The majority of modern tableware is now dishwasher safe. New plates usually have glazing over the decoration, so the pattern will not fade.
Older or hand-painted items won't have a protective glaze, so will fade over time even through hand washing. You can tell if an item is not glazed by feeling for a slightly raised pattern. If in doubt, wash by hand.
Check manufacturers' instructions to see whether items are suitable for the microwave, oven or freezer. Any gilded pieces will not be safe in a microwave.