Nothing very scientific, I'm afraid, but I do have my favourites from this period. Of course, Hilbert, but in addition: Élie Cartan, Emmy Noether, Hermann Weyl, Paul Dirac (if one is allowed to consider him a mathematician), Kurt Gödel, André Weil, Israel Gelfand, Laurent Schwartz. And I'm sure that I'm leaving many in the inkwell, so to speak.
A more scientific approach -- I'm fully aware of its pitfalls! -- is that given our propensity for naming things after people, one could draw a list by counting attributions using the Encyclopaedia of Mathematics or the Princeton Companion as corpus.
Edit
OK, this time $\epsilon$ more scientifically. I took the PCM The Princeton Companion to Mathematics (don't ask), converted the PDF to text, analysed the word frequency and isolated the names mentioned among the answers thus far. I then fed the results to Wordle and obtained the following amusing name cloud:
I've also made available a larger PDF version of the image. Needless to say, one has to take this with a grain of salt. It's a first approximation. For example, no effort has been made to distinguish between Cartans, Artins, 'von Neumann' actually denotes the appearances of 'Neumann'. Not to mention the fact that as Greg points out in a comment below, it is heavily biased in favour of those mathematicians after whom we name things. But I take it we are aware that any such lists are bound to have an element of bias and subjectivity.
