Jonathan Tisdall, Improve Your Chess Now (1997) offers two useful appendices: "Mating Patterns" and "Common Tactical Themes." His words describing "Double Attack/Check" echo a statement that recall from Yuri Averbakh, Chess Tactics for Advanced Players (1992).
Double Attack is the essence of any successful operation. It would be more accurate to say Multiple Attack, since there is often a presence of, or a need for, more. I imagine the wording has arisen because a double is the limit on checking. Almost all the other themes have some element of multiple attack contained in them.In his largely successful effort to advance middlegame theory, Averbakh highlights the centrality of the double attack.
Tisdall, Improve Your Chess Now, 204.
If we regard the term "double attack" in a broader sense than has been done up to now by theoreticians, namely not merely as a two-pronged attack, but as a combination of attacks and threats, we notice that the double attack in one form or another in the basis of most intricate tactical operations.Averbakh's brilliant discussion of how the elementary checkmate of a lone king through the coordinated actions of a queen and king illustrates the double attack in practice is sufficient reason for paying the price to acquire a copy of this classic text. Averbakh's clear discussion of contacts also informs, it seems to me, the thought-provoking efforts of Momir Radovic to challenge the way chess is ordinarily taught to beginners, and to offer a system grounded in sound pedagogy.
Averbakh, Chess Tactics for Advanced Players, 6.
It is almost possible to extract a list from Averbakh's text through examination of subheadings. However, most of his terms are better described as meta-motifs, efforts to make a theoretical contribution in the understanding of types of contacts. It is not Averbakh's central purpose to develop a practical list of motifs. Here's a sample of his headings.
Two-fold attack on a defended piece
Two-fold attack on two targets
Two-fold attack in conjunction with a pin
Mutual two-fold attack
Two-fold double attack
Tisdall offers an abbreviated theoretical discussion in the process of defining the terms in his list.
Demolition of Pawn structure
The index to Lev Alburt and Al Lawrence, Chess Training Pocket Book II (2008) offers another list. Some of the motifs are better described as positional, rather than tactical.
Removing the defender
The training website Chess Tempo uses a tagging system whereby users identify the motifs in problems, or can vote motifs others have identified up or down. The CT list currently has 34 tactical motif tags.
Back Rank Mate
Weak Back Rank
I have previously compiled a practical list in the creation of workbooks for my chess summer camps. The list is far from complete, but highlights those that I easily find in historic games from which I extract training positions for youth players to solve.
Removal of the guard
Edit 24 June 2014:
This year's camp workbook added zwischenzug, as well as discovered check as a separate entry.