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The LaTeX Wikibook writes:

Please understand: you do not have to use floating tables. It only looks more professional. If you want to place your tables where they lie in your source code, do not use table at all! This is a very common misunderstanding among newcomers.

LaTeX works with an intricate table placement algorithm, but I often prefer immediate placement with the H placement specifier (enabled by the float package).

My understanding is that captions and table/figure numbering require the table/figure environments. Is this really so, or are there ways around that? What other reasons are there for using table/figure if we know that we don't want a particular object to float?

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My opinion is that if something can't be allowed to float, then it doesn't need a caption. The purpose of the caption is to provide a description for something that can be far from the text referring to it; a graph or table that can't float has its description in the text around it. – egreg Jul 10 '13 at 10:49
@egreg (a) Maybe you have a bunch of tables in close succession showing trade statistics for 2 or 3 countries. Having the country name in a caption seems like a good idea. (b) It can be nice to have all table- or figure-like material be named and numbered, even if it doesn't float. One aspect of this is that this will provide an easy way to index the material (in a list of tables/figures/whateveryoudliketocallit or in the index of a book) and refer to it by number. – Lover of Structure Jul 10 '13 at 12:08
@egreg -- floats typically insert space around the floating object. if a table happens to be the first (or perhaps only) thing in an appendix, this spacing and other features of the float interfere seriously with the positioning relative to the appendix header. that does not always remove the need for a table caption. – barbara beeton Jul 10 '13 at 13:22

It is too long as a comment. capt-of package documentation says as follows.

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