The Collaborative International Dictionary of English v.0.48:

Seaweed \Sea"weed`\, n.
   1. Popularly, any plant or plants growing in the sea.
      [1913 Webster]

   2. (Bot.) Any marine plant of the class Algae, as kelp,
      dulse, Fucus, Ulva, etc.
      [1913 Webster]

WordNet (r) 3.0 (2006):

seaweed
    n 1: plant growing in the sea, especially marine algae

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "seaweed":
   algae, autophyte, bean, bracken, brown algae, climber, conferva,
   confervoid, creeper, diatom, fern, fruits and vegetables, fucus,
   fungus, grapevine, green algae, gulfweed, herb, heterophyte, ivy,
   kelp, legume, lentil, liana, lichen, liverwort, mold, moss,
   mushroom, parasite, parasitic plant, pea, perthophyte,
   phytoplankton, planktonic algae, plant families, puffball, pulse,
   red algae, rockweed, rust, saprophyte, sargasso, sargassum,
   sea lentil, sea moss, sea wrack, smut, succulent, toadstool, vetch,
   vine, wort, wrack