I don’t think there is a general rule. Personally, I (as a technical translator) go by the following: The longer the word, the better it is to use a hyphen, such as counter-clockwise. This is also recommendable for double-R as in counter-rotation. The more common the word is, the easier it is to write it together, especially if it is short such as counternut. Otherwise, it simply depends on the word’s respective common usage.

In general, BE tends to hyphenate more frequently than AE (or to retain the hyphen longer). Dictionaries are a good place to start -- M-W and AHD for AE spelling, Oxford and Collins, etc. for BE spelling. Contrary to #1, in all of them, it's spelled "counterclockwise" (in the BE dictionaries, of course, it's listed as AE, with "anticlockwise" being the BE equivalent).

Your're right, hbberlin, counter-clockwise is not such a good example, because even though it may well be written with a hyphen (e.g. https://en.wiktionary.org/wiki/counter-clockwise, http://www.dict.cc/?s=counter-clockwise) it is commonly written as one word counterclockwise.