Are there any hard-fast rules on when to use or not use the donojiten (々)? I find that it is used for repeating the previous character (e.g. 人々).
Other than helping me distinguish whether a text is Japanese or Chinese (never found it) I don't know where else it is used or when it shouldn't be.
Yes, the purpose of this character is to indicate a repetition of the previous kanji.
In practice, I find it's mostly just used for the relatively small class of words that are made up of a single kanji reduplicated (so 人々{ひとびと}, 我々{われわれ}, 度々{たびたび} and so forth). These words are almost exclusively written using the 々 character, and it's rare (if not incorrect) to see both kanji written out in full.
It also appears in words where the same kanji is repeated to indicate iteration in meaning, such as 翌々日{よくよくじつ} "the day after next" and 明々後日{みょうみょうごにち} "the day after the day after tomorrow". Note that the latter is a somewhat special case, as its kanji are commonly used as ateji for its synonym 明々後日{しあさって}, including the 々, even though in this case there's no actual repetition in the pronunciation.
Outside of special cases such as that ateji usage, though, you'll only generally see 々 in words where both the kanji and its reading are repeated (rendaku notwithstanding). Words with repeated kanji which use separate readings, such as 日日{ひにち}, don't use the symbol (though other conventions may be used to avoid confusion instead - that word in particular is commonly written as 日にち).
I agree with Ben's answer, and will add for comparison the following:
日々（ひび）
日日（ひにち）
When the repeated kanji has a different reading, the mark is generally not used.
There are a lot of examples where the donojiten mark ('noma' for short, by the way) represents a voiced consonant, such as in 様々、隅々、時々, etc.
I suspect the noma mark may be in a transitional phase where it will eventually become obselete, as with some of the other odoriji characters like 〆、ゝ、〳 etc. But for now, you can use it whenever the initial kanji is to be repeated, unless the reading completely changes. And it can be used when the second kanji represents an example of rendaku as well.
