This form of eavesdropping became common practice with rulers from many cultures. In English, the phrase "the walls have ears" was first recorded in its present form in the mid-1600s. (From "Shhh! The Walls Have Ears!")
Does it mean 'by'?
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It simply means 'among'.
Rulers from many cultures commonly practiced this form of eavesdropping.
Another paraphrase of with in this context might be attending or accompanying.
A problem with|attending high-performance cars is that they need very frequent tune-ups.
A problem that accompanies high-performance cars is that they need very frequent tune-ups.
Much the same idea can be expressed with the possessive:
The problem with him is that he gives up too soon.
His problem is that he gives up too soon.
This form of eavesdropping was the common practice of rulers from many cultures.
In this exact sentence, especially in translation, the best parallel would usually be for or of
This form of eavesdropping became [the] common practice for/of rulers from many cultures.
but, like CinCout said, that's because the real sense is among: It was a practice common among/shared by that group of people. That use in turn was based on Tromano's: It was a practice that was often found among that group of people. Note how Tromano adjusted his own repetition of the sentence without quite noticing how he was changing both it and his answer.