For the sake of metahistorical accuracy (and for fun), what would a distillation of Pete's excellent list (and perhaps Greg's bookends, plus the stragglers in the 1840s) to a shortlist of 15 or 20 look like? This would better match the "density" of mathematicians in the later part of the era Bell covers, after all.
My humble proposal (not including Cantor, Kovalevskaya, and Poincaré, who are in Bell already):
Lie, Klein, Hausdorff, Hilbert, Minkowski, the Cartans, Hardy, E. Noether, Weyl, Littlewood, Ramanujan, Banach, von Neumann, Kolmogorov, Godel, Weil, Mac Lane, Turing, Erdos, Feynman.
That's 20, counting Elie and Henri Cartan as one a la the Bernoullis. In attempted keeping with the flavor of the original, I gave special consideration to mathematicians whose life could be "romanticized" to some degree, hence the inclusion of von Neumann, Turing and especially Feynman.
Thoughts? Keep in mind that I'm trying for "original flavor," so look at biographical considerations as well as mathematical, and play nice.