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I want to say that it's possible that at least one of {A,B} is true, and possibly both of them are true. Is it correct to phrase it as "either A, or B, or both are true".

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Typically you would list them in order with commas and leave off "or" until the last item, as in:

"either A, B or both are true"

Keep in mind that there are those who prefer a comma after B as well:

"either A, B, or both are true"

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    Either is typically reserved for two options. Some people will object to using it for three, as in your examples. (Whether or not they have a point, is a separate issue, it's just something to be aware of.) – RegDwigнt Sep 22 '13 at 12:44
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Usually just "A or B" implies what you want, but if you want to clarify that meaning is not exclusive, you can use and/or.

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Mathematical logic speaks of an exclusive-OR and an inclusive-OR. Typically parents offer exclusive-OR choices to their children. ("You can have either cake or ice cream"; "...but not both" is implied.) You can say "Either a or b, but not both" to clarify an exclusive-OR, or "Either a or b, or both" to clarify an inclusive-OR. The "but not both" or "or both" in a sense wraps around the whole "either a or b" part.

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Since "or" is neither logically or commonly exclusive, "A or B" expresses exactly what you're aiming for. If you're getting into troubles about clarity I would suggest rephrasing the particular sentence in a way that leaves no doubt:

Maybe I will open the door to my right or my left

could translate to

I might open any of those doors

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The multiple form would be: 'Any or all of A and B are true.'

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