Can you use different kinds of breakers in a breaker box?

The NEC says you can only use equipment being used as it was submitted and approved by UL. Most breakers are not tested for other brands of panels. Even Murray MP120 and Siemens Q120 which look identical and are made by the same company are not UL listed to be used interchangeably. So to generally you need to match brand and model.

There are exceptions, brands that are out of business, like Zinsco, there are companies that make breakers for these panels and get them tested for the purpose, these are legal for use.

There is also a UL class of breaker called "classified", on the front of the breaker they will have the words "classified product" in a small circle. They are generally perceived negatively in the service trades, but they are acceptable by code to be used in panels they have been tested for. For Instance this breaker http://www.amazon.com/gp/product/B0058I3204/ref=as... is approved for several brands, including both the MP120 and Q120 mentioned earlier.

Some companies such as Square D object to use of classified breakers and claim warranty exclusion for their load centers if classified breakers are fitted in them.

yes, there are several brands that will interchange, however by NEC standards you can only use the breakers that are listed on the panel for use. A good practice is to always use the same brand of breaker as the panel.

There are a few brands that interchange, but for the most part different brands fit differently and cannot be used.

Yes, if they are compatible with the panel box. Otherwise, no.