"Toom-3 is asymptotically O(N^1.465), the exponent being log(5)/log(3), representing 5 recursive multiplies of 1/3 the original size each. This is an improvement over Karatsuba at O(N^1.585), though Toom does more work in the evaluation and interpolation and so it only realizes its advantage above a certain size."
Reading http://gmplib.org/manual/Multiplication-Algorithms.html, it appears that GMP implements: Karatsuba, Toom-3, Toom-4, Toom-6.5, Toom-8.5, FFT -based multiplication methods, which I interpret to mean that Toom-Cook is useful for ranges between where Karatsuba and FFT are most useful.
http://gmplib.org/devel/log.i7.1024.png
More context and explanation can be found at: http://gmplib.org/devel/
Short summary: Toom-Cook is nice because you have many parameters to play with.
For me this falls into the category of "new to me, but it's old news if you're in the field."