I've been working on a GUI for typesetting tensor/monoidal diagrams in TikZ.
It's especially geared at applications to quantum mechanics, namely "dot"-style diagrams of Frobenius algebras for complementary observables (Coecke, Duncan, arXiv:0906.4725) and entangled states (Coecke, me, arXiv:1002.2540).
Given Dave's already quite extensive list of what's out there on the monoidal side of things, I can only really refine what he's said.
Bob Coecke's short book (or long paper :-P) "Categories for the Practising Physicist" gives a pretty gentle buildup from physical principals, through Dirac notation for QM, to graphical notation, explaining some of the intuitions along the way.
I found Ross Street's slides on Frobenius algebras to be a quick and easy (though sketchy) intro to the topic:
The contemporary paper (Street. Frobenius monads and pseudomonoids. J. Math. Phys. (2004) vol. 45 (10) p. 3930) is very good, but considerably more technical, as it works in the language of higher categories.
I just realised that John's paper, "A Prehistory of n-Categorical Physics" hasn't been mentioned. This one puts the whole monoidal/graphical physics thing in a historical context starting from Maxwell and going through Feynman, Penrose, Mac Lane, Joyal, and all the other usual suspects. This is a long one, but it seems quite comprehensive.