Alfred R. Wallace: (British, 1823-1913) The "biggie" in zoogeography. More than any other, Wallace (as well as being the co-founder of the principle of natural selection), compiled many observations (often made by others) on distributions, diversity, extinction, disjunctions, climate effects on distribution, etc) into a series of major works that summarized his ideas (The Malay Archipelago, The Geographical Distribution of Animals, and Island Life) all between 1869 and 1880. He refined and extended Sclater's regions to other groups of animals with the idea that concordance in distributional patterns in distinct taxa substantiated the reality of those divisions and the processes that generated them (i.e. hard to imagine they could result from random processes when they influenced the distribution of so many independently evolving groups). This impact is perhaps most famously indicated by the recognition of "Wallaces Line" which separates faunal of southeast Asian origin and affinities from those in Australia.

A figure from Wallace's book showing faunal regions in southeast Asia and Wallace's line (in black)
A further development in this time periods were several "rules of biogeography" originating pre-1900's that stem from observations of geographical trends in species and their attributes:
Bergmanns Rule (1847). Body size of taxa tends to increase with increasing latitude
Allens Rule (1878). Species at higher latitudes tend to have shorter, smaller limbs than those at lower latitudes.
Jordans Rule (1881). Fish species/populations (i.e., ectotherms) from higher latitudes have more and smaller vertebrae than those from lower latitudes.
Such "rules" (there are of course exceptions) stemming from biogeographic observation helped stimulate the field of physiological ecology and understanding how environment (temperature as a correlate of latitude) and physiology (heat loss through body volume/surface relationships) could influence geographic variation in species attributes (e.g. body size, colouration, etc).
(iii) 1900-1960
The chief development during this period with relevance to biogeography was the "evolutionary synthesis" (roughly during the 1930-40s) when classical Mendelian genetics, theoretical population genetics, systematics and taxonomy were more-or-less unified into a comprehensive body of theory of evolutionary change. Scientists such as J.B.S. Haldane, S. Wright, and R.A. Fisher merged transmission genetics with mathematical theories of how factors such as genetic drift, mutation, and natural selection could drive evolutionary change (they provided, for instance, the "nuts and bolts" of Darwin's NS mechanism). Scientists such as T. Dobzhansky (experimental genetics in Drosophila populations) and E. Mayr (systematics and biogeography, principally in birds) helped to promote the idea of geographic isolation in the origin of species. Notably Mayr, in Systematics and the Origin of Species (1942), made extensive use of biogeographic observations to argue that geographic isolation was critical for speciation (i.e. the "allopatric" model of speciation). Because these workers highlighted the examination of geography in speciation and species diversity they helped cement a close relationship between biogeography and evolutionary biology. This raised the profile of biogeography because as stated by Dobzhansky, "Nothing makes sense in biology except in the light of evolution".
(iv) 1960-present
Four key developments charged the maturation of biogeography over the last 40 or so years (and continue today!)
(1) Development and substantiation of the theory of continental drift and plate tectonics first articulated most notably by the German climatologist, Alfred Wegener and an American geologist, F.B. Taylor earlier in the century. Obviously, continental drift has huge implications for reconstructing the origins of biogeographic patterns, area of landmasses, climate changes, opportunities for geographic isolation, ages of islands, etc.
(2) Development of "Phylogenetic systematics". Willi Hennig, a German entomologist, developed (first published in English in 1966) the philosophy and basics of reconstructing the historical relationships amongst taxa that are so crucial for much biogeographic inference. As we will see, the methodology placed methods for understanding the diversification of a lineage within a concrete evolutionary (process-driven) framework. This reinvigoration of basic systematic research had the correlated effect of stimulation of using these "phylogenies" to understand the relationships among geographic areas and how their relationships and history might influence the evolutionary history of their biotas and stimulated much research in "vicariance biogeography".
(3) The rise of "ecological biogeography". The historical nature of processes influencing biogeographic patterns had been the focus until the mid 1960s when ecology began to increase in prominance as a field in biology. R. MacArthur and E.O. Wilsons theory of island biogeography (1963, 1967) focussed on islands as special places to study the influence of contemporary ecological processes in determining species diversity, composition, and abundance. They articulated a theory that related characteristics of islands (variation in size, isolation, habitat diversity) and of the processes of extinction and immigration to explain biogeographic patterns in species distributions. This work reprsented a "paradigm shift" from species distributions being "static" to them being equilibrium conditions resulting from the balance between opposing forces.Technological advances.
(4) Advances in computer technology (heck, just the invention of computers!), satellite imagery, Geographical Information Systems, geophysics, and recombinant DNA technology (e.g. the green turtle example in intro lecture) all have allowed old hypotheses to be tested rigorously and expanded the spatial scale of biogeographic inference.
The growth of biogeography over the last 40 years is reflected in the tremendous growth in primary journal publications over the same time period and the founding of a journal dedicated to biogeographical analysis (Journal of Biogeography, 1973). Of course, many publications of direct or indirect relevance to biogeography also occur in other related journals (Science, Nature, Evolution, Molecular Ecology, Conservation Biology, Ecology, Geology, etc.) Try doing a search using Ovid with "Biogeography" in the key words and youll see what I mean!
References:
1. Brown, J.A. and M.V. Lomolino. 1998. Biogeography. 2nd edition. Sinaeur Associates. Chapter 2.
2. Mayr, E. 1982. The growth of biological thought. The Belknap Press of Harvard University. Good source for biographical sketches of individuals.
3. Quammen, D. 1996. The song of the dodo : island biogeography in an age of extinctions. New York : Scribner. Great treatment of some the life and times of A.R. Wallace and some of the more recent personalities in biogeography.