The most common alternative to taxonomic classifications are functional classifications. Emphasizing ecological similarities rather than similarities in relatedness, they can be regarded as complementary approach to, but not as a replacement of taxonomy. Why do we need this? Because species often perform very similar tasks, exhibit very similar characteristics and, most importantly, are very, very numerous (there are ~ 300,000 vascular plants). Reducing this redundant complexity is crucial for decision-making in conservation politics or the projection of vegetation change under future climatic conditions (Woodward & Cramer, 1996).
The idea behind this is to use functional traits, such as seed size, height, photosynthetic pathway, root density, etc., as a surrogate of a species' ecological 'role' -- its response to environmental factors and its impact on ecosystems. Seed mass for example (functional trait), is a proxy for the dispersal ability of a plant (function, performance). You should have a look at <PERSON> et al. (2007), there is a nice table (too big to include here) that links specific traits to the actual ecological functions they describe. But look at this figure from the same paper:
By applying multivariate statistics like cluster analyses or ordination methods, species can then be classified into functional types. To make up one example, a functional type that might emerge from species with the following traits
* height: > 20 m
* seed size: > 0.5 cm
* woody: yes
* Specific leaf area: low
would certainly represent climax forest trees. This classification does not distinguish between individual species, because, from an ecosystem perspective, they all are functionally roughly equivalent.
For further research google 'Functional trait', 'Plant functional type' or have a look at refs 3 and 4.
Citations:
1. <PERSON>, F. I. and <PERSON>, W. (1996): Plant functional types and climatic change: introduction. Journal of vegetation science, 7(3): 306–308.
2. <PERSON>, S., <PERSON>, S., <PERSON>, J. H. 3
C., <PERSON>, E., <PERSON>, S. P., <PERSON>, S., Pausas, J. G., Pérez-Harguindeguy, N., <PERSON>, C., and <PERSON>, C. (2007): Plant Functional Types: Are We Getting Any Closer to the Holy Grail? In: Canadell, J. G., <PERSON>, D. E., and <PERSON>, L. F. (editors): Terrestrial Ecosystems in a Changing World, Global Change—The IGBP Series, pages 149–164. Springer Berlin Heidelberg.
3. <PERSON>, S. (1990): A morphological classification of plants, with special reference to the New Zealand alpine flora. Journal of vegetation science, 1(3): 291–304.
4. <PERSON>, M. R. and <PERSON>, M. (1992): Classifying plants into groups on the basis of associations of individual traits–evidence from Australian semi-arid woodlands. Journal of Ecology, 80: 417–424. 495