Zeugma and syllepsis
are closely related, and these days zeugma is the general term used to cover both. Traditionally, both terms have a rhetorical
use (one concerning word choice) and a grammatical
use (one concerning agreement). Webster helpfully gives Latin examples for the grammatical uses.
In the traditional distinction, the examples quoted by Footprints above are of syllepsis, not zeugma. The difference is that in syllepsis the word being applied more than once is correct for both individual uses, whereas in zeugma the word is correct for one yokefellow but strictly not for the other.
An example of narrowly-defined zeugma is "with weeping eyes and hearts". This doesn't mean that you should expand this to "weeping hearts" literally, but that you should understand "whatever the equivalent of weeping is for hearts", groaning or agonizing perhaps. Another example is "See Pan with flocks, with fruits Pomona crowned" -- the goddess Pomona may be conceived of as literally crowned with fruits, but for Pan you have to supply some equivalent for flocks.
A third example, often quoted, is in Henry V, Act 4, scene 7, where the Welshman Fluellen (hence "poys" for "boys") exclaims with horror at what an army has done contrary to the rules of war: "Kill all the poys and luggage!". -- They killed the boys and did something equivalent, like sacking it, to the luggage.
Contrast with true syllepsis, where the word applied is indeed appropriate to both, but with a shift of meaning. Another classic example is also from Dickens, the woman who "departed in a flood of tears and a sedan chair". This use is usually humorous, since it seems to violate grammar to use the one word "in" for two different meanings simultaneously.
Another form of zeugma (or syllepsis?) that is grammatically questionable is when different inflected forms of the verb are called for, but only one form is used and implicitly repeated. For example, "Mary went there yesterday and I shall tomorrow", where you need to supply not "went" in the second clause but "go". Or, "We can and have seen it", supposedly a contraction of "We can see it and have seen it", but it reads as if it's a contraction of "We can seen it...".