Do compression tables exist and where are they used?
The big advantage of Lempel-Ziv-style compression is that


it creates its own dictionary on the fly and
tailors it to the data. Therefore, they are
general-purpose compression algorithms which
can be used without having to keep dictionaries in sync; all you need for
decoding is the encoded file and the algorithm.


If you fix a dictionary, this is going to perform well for some inputs. For instance, you can order all English words by frequency in some corpus, number them and store a sequence of these numbers instead of the words themselves. This will then work very well for English texts similar to your corpus, worse for other texts, and not well at all for weather data or images.

Note that LZ-style compression is used in popular formats such as (g)zip, PNG and GIF.

FLAC is one noteable format that uses something different, namely linear predictors. In a certain sense, you can view this as a fixed (though conceptually infinite) dictionary; the method estimates parameters of a certain model and represents bits of data by these parameters (plus some error information). This works well because the model fits the kind of data (apparently) very well, and the representatives are significantly smaller than the data itself. However, the decoder only knows the model; there is no fixed set of parameters everybody uses. So I don't think this fits your idea, either.