First, some textbook cardboard. Our current taxonomic systems date their academic heritage back to Carl Linnaeus, who in his Systema Naturae adopted the concept of dividing organisms (and minerals) between hierarchically-nested categories, the "ranks" of class, order, genus and species, with the last two ranks together representing the individual name of a given species. As a result, the nomenclatural system most widely used today is generally referred to as the "Linnaean" or "rank-based" system. Through various circumlocutions, this system has given rise to our current codes of nomenclature, which all share two main priciples relevant to this post - taxa are divided between nested hierarchical ranks, and each ranked taxon has a type (genus or species) at a lower rank whose inclusion is a pre-requisite in defining the concept of that taxon. The Zoological Code only covers taxa up to the ranks of family and superfamily and does not regulate higher ranks, while the Botanical and Bacterial Codes cover taxa up to class (Bacterial) or phylum (Botanical) level. Beyond these basic pre-requisites, the Codes are actually quite free and easy. The Codes demand that a "family" must be a subset of an "order", and not the other way around, but there is absolutely no official guideline as to what degree of divergence constitutes an "order" or a "family". For instance, humans have been included by many systematists in a family Hominidae separate from the great apes in the family Pongidae. However, it is now widely accepted that some of the apes are actually more closely related to humans than to other apes - specifically, that chimpanzees and humans form a clade that excludes gorillas, while all three form a clade that excludes orangutans. Some authors have represented this change of concept by including great apes and humans in a single family Hominidae, with a subfamily Ponginae for the orangutan and Homininae for humans and African apes. Others would retain the family Pongidae for the orangutans only, while placing the remainder in the family Hominidae divided between the Gorillinae (gorillas) and Homininae (humans and chimpanzees). Still others might divide the chimpanzees in a separate subfamily from humans. The thing is that the current systems of nomenclature make absolutely no distinction between these various set-ups. All the available options satisfy the basic requirements - subfamily Homininae (if used) is a subset of family Hominidae, and Hominidae always includes the genus Homo. Beyond that, the only thing determining which option an author uses is their own personal judgement on how different a human is from a chimpanzee. Consider, also, the following figure from Baum et al. (1998) (click on it to see a larger figure):
This figure shows phylogenetic relationships within the "core Malvales", a clade of flowering plants previously divided between the families Malvaceae, Bombacaceae, Tiliaceae and Sterculiaceae, but for which all families except Malvaceae had turned out to be para- or polyphyletic. The figure shows four alternative methods of re-classifying the core Malvales in light of improved phylogenetic understanding. The point is that despite the siginificant differences in appearance between the alternative systems (recognising from one to nine families, two to nine subfamilies, etc.), there is actually no difference in the underlying phylogeny. Nevertheless, all four classifications are equally valid because all four meet the requirements of the rank-based system of nomenclature. Because there is no philosophical underpinning to what each "rank" means, the only guideline is a sense of tradition about what has been referred to a certain rank in the past - and because workers on different groups of organisms have different traditions, this is meaningless. As pointed out by David Marjanović in the comments at Tet Zoo, ranks can be (and, all too often, actually are) actively misleading because the temptation to assume that a "genus" of insects is somehow directly comparable to a "genus" of rodents has proven irresistible far too often in the past. Take another look at the Baum et al. figure above. Is "subfamily Malvoideae" in option C a less significant taxon than "family Tiliaceae" in option A?
Problems have also arisen in rank-based nomenclature because of the sheer number of ranks sometimes required. Kingdom, phylum, class, order, family, genus and species is easy enough to keep track of, but nowhere near enough to deal with the ten million or so species that infest this planet. Take something as boring and well-known as the common house sparrow, Passer domesticus. Passer domesticus belongs to the genus Passer, which is part of the family Passeridae, which belongs to the Passeroidea, part of the Eupasseri, part of the Passerida, part of the Euoscines, part of the Oscines, Eupasseres, Passeriformes, Anomalogonatae, Coronaves, Neoaves, Neognathae, Aves, Ornithurae, Ornithothoraces, Avialae, Eumaniraptora, Metornithes, Maniraptora, Maniraptoriformes, Coelurosauria, Neotetanurae, Tetanurae, Neotheropoda, Theropoda, Saurischia, Dinosauria, Ornithotarsi, Dinosauriformes, Ornithodira, Archosauria, Archosauriformes, Archosauromorpha, Sauria, Neodiapsida, Eosuchia, Diapsida, Eureptilia, Reptilia, Sauropsida, Amniota, Cotylosauria, Batrachosauria, Anthracosauria, Neostegalia, Tetrapoda, Tetrapodomorpha, Sarcopterygii, Osteichthyes, Teleostomi, Gnathostomata, Vertebrata, Craniata, Olfactores, Chordata, Deuterostomia, Eutriploblastica, Bilateria, Eumetazoa, Animalia, Holozoa, Opisthokonta, Unikonta, Eukaryota, Neomura. Try thinking up ranks for every one of that lot! Some pretty horrendous terms such as "supersubphylum" have been perpetrated in such attempts.
It is response to such issues that the concepts of phylogenetic nomenclature and rankless taxonomy arose. In phylogenetic nomenclature, a taxonomic name is defined in relation to an underlying phylogeny (Queiroz & Gaulthier, 1990). For instance, in my first example above, "Hominidae" may have been defined as the largest possible clade that includes humans (Homo) but not orangutans (Pongo). In that case, under the phylogeny given above, chimpanzees and gorillas must belong to Hominidae, while orangutans cannot. Ever. Concordant with the development of phylogenetic nomenclature has been the concept of a rankless taxonomic system. The two are generally assumed to be equivalent by many critics of phylogenetic nomenclature, but in fact they are not. Theoretically, it would be still be possible to erect a system of phylogenetic nomenclature that assigned ranks to the taxa it recognised. It would also be possible to devise a rankless taxonomic system that was not based on phylogeny but on, for instance, overall morphological similarity only. These options have not been considered because, quite simply, they would offer no advantage over the current rank-based system. A ranked phylogenetic system would have the same "too many ranks" problem of the current system, as well as problems all of its own devising if, e.g., conflicting definitions required that one "family" refer to a subset of another "family".
As an aside, I think it is also important to distinguish between the Codes of Nomenclature and the principles underlying their construction. While the rank-based system has its current codes, the (in)famous PhyloCode is in the process of being drafted to regulate phylogenetic nomenclature. The rank-based codes may have the same underlying principles, but they differ in their regulations as a result of different opinions on the most effective means of serving those principles. Similarly, whether or not the PhyloCode is adequate as a regulatory code is a separate issue from whether phylogenetic nomenclature is worthwhile as a concept.
It goes without saying that the concept of phylogenetic nomenclature has had its share of detractors, both on the front of phylogenetic nomenclature in the strict sense, and on the front of rank-free taxonomy. Of the two fronts, it is actually the first that is (in my opinion) the easiest to deal with. One of the main complaints about phylogenetic nomenclature is that it effectively eliminates the possibility of paraphyletic taxa. Take the classic example of Reptilia (reptiles), a paraphyletic "class" that actually includes the ancestors of another "class", Aves (birds). Under phylogenetic nomenclature, Reptilia must either include birds, or be abandoned as a taxon. Supporters of the rank-based systems may point at modern representatives of the two "classes" - lizards, crocodiles, birds - and argue that because crocodiles are more similar to lizards, despite being closer phylogenetically to birds, lizards and crocodiles represent a paraphyletic grade that merits official recognition. However, this ultimately comes down to a judgement call that the similarities between lizards and crocodiles are more "significant" than the similarities between crocodiles and birds. It is also largely an artifact of the extinction of taxa intermediate between the latter two. Would the division be regarded as being as "obvious" if ceratopsians had survived to the present? What about allosaurs? With any paraphyletic taxon, a point is reached where an arbitrary line has to be drawn that exagerrates the differences between taxa on either side of that line. What is so significant about the difference between Archaeopteryx and Microraptor that one should be placed in a separate "class" from the other?
Despite what might be expected, the idea of a rank-free classification is actually more problematic than paraphyly-free classification. This may make no sense at first glance, because the ranked system seems philosophically almost indefensible. The thing is that, ultimately, the appeal of the ranked system doesn't lie in its philosophical defensibility at all. Rather, the rank-based system has such a strong appeal because of its usefulness as an initial didactic and organising tool. Students find it much easier to gain and remember a quick understanding of the hierarchical relationships of taxa if they have a set of pegs to pin them on. Also, people find it helpful to have an "agreed" list of significant taxa. It is often claimed that the rank-based system is somehow more stable than the phylogenetic system, because change in phylogenetic understanding can supposedly lead to sweeping changes in the contents of phylogenetically-defined taxa. The problem is that this stability is nothing more than an illusion. Not only does it feed into the comparability error I referred to earlier, but the "agreed" list is all too often nowhere near as "agreed" as people think it is. Take Aydin Örstan's comment on the seemingly straightforward aim of seeing at least one member of every animal phylum:
But, first, I need to figure out how many animal phyla there are. However, that is not an as easy task as it seems. Wikipedia lists 36, the Animal Diversity Web lists 32 and the University of California Museum of Paleontology gives 25 extant animal phyla.
The phylogenetic system is indeed prone to change with changing phylogenies, but so is the rank-based system. What is more, as shown in the Hominidae and core Malvales examples above, there doesn't even need to be a change in phylogeny, only a change in an individual author's perception of the "significance" of differences.
Overall, I have (initially somewhat reluctantly) come to the conclusion that from a philosophical position, phylogenetic nomenclature knocks down the rank-based system without even breaking a sweat. This does not mean that we should all be rushing headlong to embrace PN - I said at the very beginning of this post that there is cause for caution. The primary handicap of phylogenetic nomenclature is simply that it requires a pretty good understanding of phylogeny (well, duh). For some groups of organisms, such as apes, we have extremely good understandings of their phylogeny. Yes, it is still possible that our views may change with increasing study, but it is extremely unlikely that, say, humans aren't closely related to apes at all but instead convergently evolved from a giant Mediterranean dormouse. For other groups of organisms, our phylogenetic understanding is more minimal. My own stomping ground, harvestmen of the superfamily Phalangioidea, represents a few thousand species of arthropod for which the classification remains almost entirely untested phylogenetically. Phalangioids are divided between a number of families, subfamilies and genera, yes, but all too often the boundaries between taxa frankly couldn't be vaguer if they had been drawn up in the back of a van by Cheech and Chong. Nevertheless, three thousand or so species is far too many to be assimilated in one hit, and the current rank-based system does allow us to break them up into a set of more manageable bits. Attempting to impose a phylogenetic classification onto phalangioids in our current state of knowledge would be a decidedly rash and hasty move, because there is no confidence that the sort of sweeping content changes that the phylogenetic nomenclature critics claim to fear wouldn't happen. A phylogenetic system for some groups of organisms remains more of a target than a current possibility.
Baum, D. A., W. S. Anderson & R. Nyffeler. 1998. A durian by any other name: taxonomy and nomenclature of the core Malvales. Harvard Papers in Botany 3: 315-330.
Queiroz, K. de, & J. Gauthier. 1990. Phylogeny as a central principle in taxonomy: phylogenetic definitions of taxon names. Systematic Zoology 39 (4): 307-322.