1) The book "2D homotopy and combinatorial group theory" (1993) is decidedly oriented towards applications and problem solving, and does discuss crossed modules in Chapters 2 and 4, and further mentions them in Chapters 5, 9 and 11 (different chapters have different authors). There are some results proved using crossing modules and not involving crossed modules in the statement. Yet I cannot refrain from quoting some honest disclaimers:

By A. J. Sieradski (p. 75):

"The difficult nature of free crossed homotopy modules limits the applicability
of the 2-dimensional homotopy classification [in terms of crossed modules]. The
cellular chain complex of the universal coverings of two-dimensional complexes
offers an abelianized version of the classification that is much more practical."

By W. A. Bogley (p. 311)

"Whitehead's work on crossed modules provides an abstract algebraic description of the second homotopy group of a 2-complex [Wh41$_1$, page 427]. Abelianizing, one obtains the homological description of $\pi_2$ in terms of Reidemeister chains [Re34, Re50, Wh46]. (See also Chapter II, Theorem 3.8, in this volume.) However, as Whitehead himself
observes [Wh41$_1$, page 409], [Wh49$_2$, page 495], neither of these descriptions
leads to effective general calculations of $\pi_2$. Nor do they shed any practical light on Whitehead's question on the heredity of asphericity."

2) D. Conduché, Question de Whitehead et modules précroisés (1996)

"The author turns [the Whitehead asphericity problem] into an algebraic question by showing that $\pi_2(Y)$ is the intersection of the terms of the lower central series of the crossed module $\pi_2(Y,Y^1)\to\pi_1(Y^1)$, where $Y^1$ is the 1-skeleton of $Y$."

3) J. Huebschmann, Braids and crossed modules (2009)

The main result of the present paper, Theorem 5.1 below, says that, as a crossed module
over itself, the Artin braid group $B_n$ has a single generator, which can be taken to be
any of the Artin generators $\sigma_1,\dots,\sigma_{n−1}$. Furthermore, the kernel of the surjection from the free $B_n$-crossed module $C_n$ in any one of the $\sigma_j$’s onto $B_n$ coincides with the second homology group $H_2(B_n)$ of $B_n$, well known to be cyclic of order $2$ when $n\ge 4$ and trivial for $n = 2$ and $n = 3$.

Topology and Groupoids(2006). It's available in e-book form for 5 pound sterling at store.kagi.com/cgi-bin/store.cgi?storeID=6FEPD_LIVE . – Harry Gindi Aug 18 '10 at 17:22