There is evidence, for one thing, that the Great Lakes sea rocket practises kin altruism, that is, it can detect related plants and treat them favorably. The study the NYT piece refers to in this regard is Susan Dudley and Amanda File's "Kin recognition in an annual plant" (pdf). Their conclusion is that
in the annual plant Cakile edentula, allocation to roots increased when groups of strangers shared a common pot, but not when groups of siblings shared a pot. Our results demonstrate that plants can discriminate kin in competitive interactions and indicate that the root interactions may provide the cue for kin recognition. Because greater root allocation is argued to increase below-ground competitive ability, the results are consistent with kin selection.In other words, these lowly seeming plants, remarkably, can somehow directly detect kin (something that has not been demonstrated in many animals) and thus they have a family-life.
Even more remarkable is the finding (also summarized in the NYT article) that the parasitic plant Cuscuta pentagona (aka dodder) uses chemical cues to detect the most desirable hosts, which it then grows towards. This finding comes from a paper ("Volatile Chemical Cues Guide Host Location and Host Selection by Parasitic Plants" [pdf]) published in Science in 2006. Watching the time-lapsed video (.mov file) of this behavior (and it is most definitely behavior) really gives one a new perspective on plants.
There is even a Society for Plant Neurobiology! (Yes, that's neurobiology). The locus classicus of this emerging field seems to be Bremmer et. al.'s "Plant neurobiology: an integrated view of plant signaling" (pdf) that appeared in Trends in Plant Science in 2006. They defined the field as follows:
Plant neurobiology is a newly focused field of plant biology research that aims to understand how plants process the information they obtain from their environment to develop, prosper and reproduce optimally. The behavior plants exhibit is coordinated across the whole organism by some form of integrated signaling, communication and response system. This system includesWhile I suspect some of this is a tad overexcited rhetoric and while these ideas are controversial (pdf), they're certainly stimulating and exciting. If the research holds up, plant neurobiology promises to transform our view of a large segment of the natural world and, as has happened repeatedly in Western intellectual history, we will have to abandon a view dominant since Aristotle.
long-distance electrical signals, vesicle-mediated transport of auxin in specialized vascular tissues, and production of chemicals known to be neuronal in animals. Here we review how plant neurobiology is being directed toward discovering the mechanisms of signaling in whole plants, as well as among plants and their neighbors.
(See also: an NPR podcast on the dodder's abilities)