Plants have hormones, just as animals do. Plant hormones, however, are chemically quite different from animal hormones. Most are small molecules, while animal hormones are often very large molecules, such as steroids or proteins. Plant hormones fall into several different categories:
Auxins -- growth stimulating hormones
Produced by apical meristems (primary growing tips) to suppress growth by lateral meristems (secondary growth buds)
I.e., these hormones repress branching
Stimulate root growth. These are the active ingredients in rooting preparations used by horticulturists and gardeners
Indoleacetic acid
Indolebutyric acid
alpha-Naphthylene acetic acid -- a synthetic auxin
2,4-D herbicides -- super-auxins
Cytokinins -- growth stimulating hormones
Antagonize the effects of auxins
Stimulate the growth of secondary branches
Kinetin -- a synthetic kinetin
Benzyl-amine purine (BAP) -- a synthetic kinetin
Abscisic acid (ABA)
Stress response mediator
Dormancy initiator
Ethylene
A gas, CH2=CH2
Stimulates ripening
Giberellic acid (GA)
Cell elongation stimulator
Dormancy terminator, so used by horticulturists to stimulate seeds to germinate