Before I start this post, I should note that this is simply a line of speculation I've had running through my head recently. I have no idea how accurate this is, or whether I'm just spouting a load of hooey. Either way, I think the question is an interesting one.
Why are there so many more species of animals than plants? More than 1.2 million species of animals have been described on this planet to date, as opposed to only about 300,000 species of plant. Even if one allows for differing species concepts, as yet undescribed species*, etc. there is no question of measuring error - animal species outnumber plant species more than four to one. Also, while most animal species tend to have clear distinctions from their closest relatives, plant species have a greater tendency to bleed into each other, with less clear boundaries (The same is also true of other non-animal eukaryotes and prokaryotes. Animals are the wierd ones in this regard). A comparison between animal and plant fossil records shows significant differences as well - even when they first arrived on land, plants never underwent an equivalent of the animals' Cambrian explosion. Plant evolution has been a far more sedate affair, with the divergences of the major modern taxa more spread out in time.
*Of which there are probably a higher proportion of animals than plants, anyway. Plants are generally easier to study in terms of biodiversity because they don't usually run away.
These points all suggest that speciation tends to happen differently for animals and plants. Why should this be? At least one major factor, I suspect, is that unlike most plants, most animals engage in active behaviour. Mobility is the key to the animals' evolutionary diversity. In most animals, reproduction happens through more or less direct copulation. As such, animals have a direct choice as regards whose gametes they fertilise or are fertilised by. Plants, in contrast, use more indirect means - wind pollination, or intermediary pollinators. As a result, their control over their fertilisation is more limited. Even in those species pollinated by insects and other animals, pollinator specialisation seems to play little part in speciation, and most pollinators are not hugely discriminating in their visits (Waser, 1998).
Speciation is the process of isolating gene pools. The differences between controlled fertilisation in animals versus more uncontrolled fertilisation in plants means that speciation in animals tends to be an active process, while that of plants tends to be a passive process. Changes in mate choice can lead to rapid speciation - for instance, they were probably a major factor in the evolution of the cichlid species flocks of the African Great Lakes*. For those organisms in which mate choice is not generally a factor, speciation is more likely to occur as a result of stochastic processes such as genetic drift. Isolating factors between species will develop with less frequency, and those barriers that do develop are likely to be less resilient.
*Lake Victoria is home to over three hundred endemic cichlid species, but sedimentary data indicate that the lake itself has only been there in its present incarnation for the last 12,000 years or so (Johnson et al., 1996). That implies the divergence of, on average, one new cichlid species every forty years.
As a test of this idea, one can look to those plants and animals that provide the exceptions proving the rules. In animals, many marine animals such as corals are broadcast spawners - they release gametes into the water and fertilisation occurs after the gametes leave the parent. Despite their worldwide distribution, corals are not a hugely speciose group of animals, with a little over two thousand known species. Or compare the diversity of the mostly broadcast-spawning bivalves (30,000 species) with the more often directly-fertilising gastropods (40,000 species).
Perhaps the most dramatic support comes from the orchids. While other flowering plants entice their fertilisers with food rewards such as nectar and pollen, orchids have developed more nefarious methods such as pseudocopulation or providing their pollinators with fragrant chemicals that the pollinators can use in their own mating displays. As a result, orchids are one group of plants for which direct mate choice is a significant factor, and speciation in orchids has boomed. Orchids include about 22,000 species, while their sister group, the remainder of the Asparagales, contains only about four thousand species all up.
Johnson, T. C., C. A. Scholz, M. R. Talbot, K. Kelts, R. D. Ricketts, G. Ngobi, K. Beuning, I. Ssemmanda & J. W. McGill. 1996. Late Pleistocene desiccation of Lake Victoria and rapid evolution of cichlid fishes. Science 273: 1091-1093.
Waser, N. M. 1998. Pollination, angiosperm speciation, and the nature of species boundaries. Oikos 82 (1): 198-201.