Heatproof glass like Pyrex and Anchor Hocking containers are best to use in a microwave. Most modern glass containers are marked as being microwave safe.
Older glass containers with bubbles in the glass are not suitable, because the bubbles can explode and cause the glass to break. To test a glass container for suitability, microwave it empty at a regular temperature for one minute.
If the container feels warm, and not hot, it is good to use. Leaded glass is also suitable for microwaves, but do not using it for foods with liquids that are acidic.
Some ceramic containers have a glaze that becomes hot in the microwave. This does not make them unsuitable for use in a microwave oven, but it does require the use of a potholder.
Glazes containing lithium, lead and barium, sometimes put on decorative ceramics, aren't safe for use in or out of the microwave. Food should never be stored in them at all.
Don't use ceramic containers with sparkles or metallic trim. Corning Ware is a suitable ceramic container for microwave use.
Baskets made of reeds, wood and straw with no metal parts are suitable for microwave use. Line the basket with white napkins or paper towels to absorb moisture and place bread or rolls inside for fast warm-ups.
Paper plates and other paper containers are fine to use in a microwave oven so long as they are white and are not foam insulated. They should not contain any plastic that melts into the food.
Only plastic containers labeled as microwave safe are suitable for use. Butter tubs and other containers sold with cold food in them are not suitable.
Chemicals in the plastic may transfer to the food when microwaved. Use only food-grade, microwave-safe plastic containers.
Not only are other containers hazardous to your health, but they also tend to melt in a microwave.