Do not put plastic containers, pans with plastic or wooden handles, plastic wrap, ceramics with cracked glaze, or glass containers not labeled oven-safe in the oven. Some of these will melt or burn; others may crack and spill their contents. Even heat-resistant glass cannot withstand sudden temperature changes; do not place a hot glass dish on a wet or cold surface.
Plastic is the clearest limit. Yogurt, margarine, and takeout containers soften, deform, and begin to melt at oven temperatures; a container labeled microwave-safe is not necessarily oven-safe, because the two appliances heat food at completely different temperatures. Plastic wrap also does not go in the oven; it melts. Oven bags made for baking are different: they are designed to withstand high temperatures and should be used according to the temperature limit on the package. A freezer bag does not go in the oven.
Handles are often overlooked. Even if the pan itself is oven-safe, a plastic handle will melt, while a wooden handle will dry out, crack, and darken over time. Pans with metal handles can go in the oven, but a metal handle coming out of the oven stays hot for a long time; leaving an oven mitt over the handle prevents the next person from reaching for it with a bare hand. For pans with silicone grips, check the temperature limit given by the manufacturer; silicone utensils must not touch the heating element directly.
For ceramic and porcelain, the measure is whether the dish is labeled oven-safe. Older dishes with cracked glaze or a network of fine lines can separate along those cracks when heated. Plates with gold or silver trim should not be used in either the oven or microwave. The trim darkens with heat and never returns to its former appearance. Earthenware casseroles should be used according to their own instructions, often by soaking them in water and starting them in a cold oven. Serving plates and bowls should not be used for heating unless they are marked oven-safe.
With glass, the key issue is the type. Heat-resistant glass dishes made for oven use can be used safely in the oven; ordinary drinking glasses, bowls, and serving plates should not be used. Even heat-resistant glass can be damaged by a sudden temperature change: do not put a cold glass dish straight from the refrigerator into a hot oven, and do not set a hot glass dish from the oven on a wet countertop or cold stone surface. Adding cold water to a hot glass dish carries the same risk; the dish can crack and break apart with its contents.
A few more items belong on the list of things that do not go in the oven. Paper towels and napkins can catch fire. Parchment paper can go in the oven, but do not exceed the temperature limit on its package, and keep its edges from touching the heating element or fan. Lids on covered dishes should be glass or metal; lids with plastic knobs will melt. If you do not know whether a dish is oven-safe, do not use it; choose an ordinary metal baking sheet or a dish made for oven use instead. Symbols and writing on the bottom of the dish can help you decide in a few seconds; if there is no symbol, do not put the dish in the oven.