Professional societies 

American Association of the Advancement of Science (AAAS)
American Fern Society (AFS)
Botanical Society of America (BSA)
California Botanical Society (CBS)
International Association for Plant Taxonomy (IAPT)
International Association of Wood Anatomists (IAWA)
International Carniverous Plant Society (ICPS)
International Society of Plant Morphologists (ISPM)
Linnean Society of London
Southern California Botanists (SCB)
The World Conservation Union (IUCN)

Plants, plant groups, and systems of classification:

NCBI Taxonomy browser  (maintained by the National Center for Biotechnology Information, NCBI)
Gymnosperm Database
The Ancient Bristlecone Pine
Angiosperm Phylogeny Website
Australian Flora on Postage Stamps
USDA Plants Database (info on 43,000+ species)
A Basic Guide to Tree Identification

Institutions in California:

California Native Plant Society (CNPS) (Sacramento, CA)
Rancho Santa Ana Botanic Garden (Claremont, CA)
University and Jepson Herbaria (Berkeley, CA)
University of California Botanical Garden (Berkeley, CA)

Institutions in the rest of the universe:

Australian National Botanic Gardens / Australian Biodiversity Information Facility
Biota of North America Program [BONAP] (Chapel Hill, NC)
Flora of North America (St. Louis, MO)
Institute of Botany and Botanical Garden, University of Vienna (Vienna, Austria)
Missouri Botanical Garden (St. Louis, MO)
The New York Botanical Garden (Bronx, NY)
Oregon Flora Project (Corvallis, OR)
Royal Botanic Gardens (Kew, England)
Smithsonian Institution, Department of Botany (Washington, DC)
The World Conservation Union [IUCN] (Gland, Switzerland)

Index herbariorum for anything else

Other links of note:

Biological Imaging Facility (The College of Natural Resources, UC Berkeley. Steve Ruzin, director)
The Golub Microscope Collection at the University of California, Berkeley
DIY Gardening and Landscaping (recommended by Eric Pruitt)