There are quite a few respectful terms for parents, the least respectful of which would be お父さん and お母さん (there are less respectful ones, but they're only appropriate for your own parents or your friends' parents). A notch above those would be 母様, 父様, お母様, and お父様. The first two are rather respectful, but I don't think they're appropriate for other people's parents; meanwhile, the second too are appropriate for the parents of people who require respect. Moving up in respect we have 母上, 父上, 母君, and 父君. I think these are 尊敬語, and a little outdated to call your own parents; are the forms in 上 or 君 more respectful? You can also add お and/or 様 for further respect: （お）父上（様）, （お）母上（様）,（お）父君（様）, and （お）母君（様）. Clearly the most respectful terms would have both お and 様, but I wonder which ones. broccoli forest mentions ご母堂（様） and ご尊父（様）; are those more respectful than anything I've listed?
Practically, you can consider お父【とう】様/お母【かあ】様 as the most polite form. It's a safe word in every formal speech, even at a wedding ceremony or funeral, as long as you don't forget the prefix お.
母上/父上/父君/母君 are mainly heard in pre-war history dramas. A few old people may use these words when they make a very formal speech, but I would avoid them. If I heard someone say one of these to refer to my parents in ordinary business settings, perhaps I can't help laughing and asking back "Wow, are you from a real ninja family?" But these would be acceptable in very formal letters.
On the other hand, when someone addresses their own parents, a very few people use (お)父様/(お)母様. Personally I know no one who actually do so (except for stereotyped rich celebrities in fiction).
御母堂/御尊父/etc are clearly the politest, but I'm sure I haven't used it in my life. I know it's mainly used in condolence telegrams and such, and that's a kind of thing for which most native speakers would search the example sentences on the net.