That's a big question. Depends on what you mean by kinds.

There's a lot of different slang terms to describe various qualities of weed. The vary a bit depending on where you live but generally:

Schwagg- crappy, low end weed
Mids- Not great but smokable.
Dank, Chronic, Dro- High end, potent weed, usually without seeds.

There's also 2 main types (species?) of weed:
Sativa-will give you an up, active, happy high, you'll laugh a lot
Indica-Tends to give you more of a heavy, body high, you'd rather chill on
the couch than do anything active, type of high. You'll say "huh?" a lot.

Then there's hundreds of different strains of sativas, indicas, and combinations of the two. Check out http://www.smokersguide.com/sg/index.html for more info on different strains