On readings are usually divided into four categories:
The first three categories represent three broad periods of borrowing from Chinese. The fourth category represents "customary" readings--generally variations on readings from the above three categories which have nonetheless been accepted as part of the Japanese language. You can read more about these categories on Wikipedia in English or in Japanese.
Some kanji dictionaries written in Japanese (called 漢和辞典{かんわじてん}) show which readings fall into which categories, but others do not; I don't know of any kanji dictionaries with English definitions that have this information. Generally speaking, larger 漢和辞典 are more likely to mark readings this way. (In addition, larger 漢和辞典 are more likely to contain less common readings.)
Here are a couple dictionaries which do mark readings this way:
- 新漢語林(しんかんごりん) (published by 大修館書店)
- 新選漢和辞典(しんせんかんわじてん) (published by 小学館)
Some 国語辞典{こくごじてん} have entries for kanji too, and some of these indicate 呉・漢・唐・慣用 as well. For example, 大辞泉 is available free online, and it has entries for some kanji, marked [漢字項目]
in the Yahoo!辞書 interface. For example, take a look at the entry for 清:
[音]セイ(漢) ショウ(シャウ)(呉) シン(唐) [訓]きよい きよまる きよめる すむ さやか すがやか
See 大辞泉の凡例 for more information.
Another online resource, as blutorange points out, is Wiktionary. I'll reproduce the example links here, in case the comment is ever deleted: 行 and 御.