Could you please provide a general guide figure out if a piece of cookware can be used in the oven, based on what material it is made of?
The usual materials used in an oven (no matter if electric or gas) are almost all food-safe non-melting materials used for cooking vessels. If you can use it on a stove top, it should be OK for the oven too (unless it has a handle from a different material).
Metal. Oven pans are made from non-reactive metals (like stainless steel) or reactive metals with a protective layer (e.g. seasoned cast iron). Don't use metal vessels which have non-metal parts, like wooden or plastic handles (except for oven-rated handles, like the phenolic handles on Le Creuset enameled cast iron, which are rated for up to 200°C). Else, all metallic pans and pots meant for stove top are good for the oven. Also, pay attention to temperature: PTFE (non-stick) coated vessels shouldn't be heated above 250°C.
Ceramics. If glazed, you should make sure that the glaze does not suffer under high temperature or does not leach dangerous chemicals into the food under high temperatures. There are many glazed ceramic pans meant for the oven, such as lasagna pans, quiche pans, tagines, gyveches, etc, and you can be sure that these are oven-safe. You can also use table porcelain for some limited scenarios, e.g. poaching an egg in an individual serving of soup, but don't risk your finest porcelain, and don't do it if the plates are decorated with adhesive designs. If unglazed, you should make sure it is intended for the oven, some types of earthenware may be damaged by the heat. The ones meant for the oven (like römertopf) should be fine.
Glass. If it is borosilicate glass (sometimes called Jena glass), you can use it in the oven. Don't subject it to temperature shocks, use room-temperature glass pans (don't layer a lasagna the day before in a glass vessel and then bake it straight from the fridge), and don't put them in too hot an oven (up to 200°C should be OK). You can't determine if it is borosilicate glass or soda lime glass from its looks, so here you have to be sure that the manufacturer markets the vessel as oven safe.
Silicone. Food-grade silicone is great for baking and practically indestructible (unless you cut it). If the manufacturer gave a temperature range, go by it, I'm not sure it will hold up at above 250°C, but it is no problem in the normal cake and pastry baking range.
Plastics. Some plastics may be able to withstand heat, but you can't usually recognize that from their looks, and you don't know if there may be other problems (such as melamine, which releases toxic chemicals when heated). In theory, I would trust a big manufacturer who markets a plastic pan explicitly as oven-safe, but in practice, I haven't seen such pans. So don't use plastic vessels in an oven.
Wood. Don't use wood in an oven. It shouldn't be able to catch fire at normal oven temperatures, so it is not a hazard, but the heat will damage your vessel. While it will still be usable (especially if you take care to wet it beforehand), it will lose its smooth surface, and it will probably warp. Glued wood can also split along the glue lines. If you have a cheap bowl you don't mind damaging, you can use it in the oven, but I don't see why, when other materials are much better suited.