The species concept is very important to taxonomists whose job it is to classify living things. I’ll use plants for examples here because I am most familiar with them but I suspect animals wouldn’t be all that different. Plant taxonomists use differences in morphological characteristics to separate and assign species. Sometimes these differences are quite small and taxonomists are not always in agreement. There are “lumpers” who ignore small differences and assign two or more closely related organisms to the same species while “splitters” would assign each to a different, although very closely related, species.
Collected specimens of dried plants are kept in a herbarium. There are many herbaria, both public and private, in various locations throughout the world. There are one or more specimens of each species designated as the “type specimen”. Curiously, the type specimen need not be typical of the species. But if the original description of the species refers to a particular specimen, that specimen is designated the “holotype” for that species.
There are sets of rules for naming both animals and plants. The International Code for Zoological Nomenclature (ICZN) is a set of rules for naming animals. The International Code for Botanical Nomenclature (ICBN) is a set of rules for naming plants. Both of these have written codes as well as governing bodies that take up taxonomic issues periodically. Just thought I would mention this in case anyone is interested.
I don't believe cladistics is going to have much effect at the species level and the next two higher taxonomic ranks- genus and family. But at the higher levels of class, phylum etc. it probably will be important. Field botanists like myself work at the lower levels- species, genus, and family- and leave the higher levels to the so-called experts who often disagree. That's why I think DNA testing will be important in sorting out some, if not all, taxonomic problems.
Some clarification why I don't think cladistics is going to have much effect on lower taxonomic levels. Plants in a single genus usually have a close phylogenetic relationship, i. e. they evolved from a common ancestor. Plants in a single family usually have a close phylogenetic relationship, i. e. they evolved from a common ancestor. So it seems to me that this is consistent with cladistics.
Since the early 20th century, Linnaean taxonomists have generally attempted to make at least family- and lower-level taxa (i.e. those regulated by the codes of nomenclature) monophyletic.
A monophyletic group is one which evolved from a common ancestor. Thus we see that under the Linnaean system of taxonomy a basis for a cladistic interpretation is in place at the lower taxonomic levels, although there are probably some exceptions.
Despite the growing popularity of cladistics, the traditional Linnaean system is not likely to be replaced in the near future.