Is there software or a website where I can browse extinct species?
You can search for species that are "Extinct" or "Extinct in the wild" at the IUCN red list website (International Union for Conservation of Nature and Natural Resources). That list currently includes 903 species, but some of the assessments might be obsolete (see annotations). From that list, you can click and get some basic information about each species.

Also note that many countries have regional Red Lists, where you can find information about regionally extinct species (i.e. species that have gone extinct in a particular country). For instance, 209 species are labelled "reginally extinct" in Sweden (http://artfakta.artdatabanken.se/, site only in Swedish), most of them insects, while still being present in other parts of the world.