TITLE: What are normalized singular chains good for?
QUESTION [14 upvotes]: One of the common definitions of homology using the singular chains, i.e. maps from the simplex into your space. The free abelian group on these can be made into a chain complex and one can take the homology of this. The result is usually called singular homology.
However, one can use a smaller chain complex instead, by taking the quotient with the degenerate chains (those that are the image of a degeneracy map $\sigma$). This will give the same result in homology.
In some articles, I've seen authors replace the singular chains with the normalized singular chains, often claiming that this is "for technical reasons" (a example is Costello's article on the Gromov-Witten potential associated to a TCFT). What are the important technical differences between these two functors? In which situations is there a preferred one?

REPLY [7 votes]: The question was about chains on a space, presumably singular chains. If what you're up to is, for example, learning or teaching the basic facts about singular homology, like homotopy-invariance and excision, then the switch to normalized chains seems like an unnecessary complication. In that context, you could say that non-normalized chains have the advantage.
To expand on Ben's comments: 
For A and B simplicial abelian groups and NA and NB the associated normalized chain complexes, there is a quasi-isomorphism $NA\otimes NB\rightarrow N(A\otimes B)$, where the tensor product of simplicial groups is defined levelwise $(A\otimes B)_n=A_n\otimes B_n$ and the tensor product of chain complexes is the usual $(C\otimes D)_n=\oplus_p (C_p\otimes D_{n-p})$. An associative simplicial ring leads in this way to an associative differential graded ring. 
Another technical advantage of the normalized complex is its role in proving that homotopy groups of a simplicial abelian group are homology groups (Dold-Thom Theorem).