Here are fun maps of generic names for waterways...

- for the U.S.: Derek Watkins: "Inundated with placenames"

river
creek
   (these first two, being the most common, are in the background with gray lines)
branch
run
fork
brook
kill
stream
bayou
swamp
slough
wash
cañada
arroyo
río

- for Britain: SpatialAnalysis.co.uk: Naming Rivers and Places

burn
brook
afon
water
river
canal

There are various interesting notes in the posts and the comments for each of these.

One of the questions arising: why is "brook" so pervasive in New England, when it's relatively sparsely used in old England?

The Online Etymology Dictionary says

"small stream," O.E. broc "flowing stream, torrest," of obscure origin, probably from P.Gmc. *broka- which yielded words in Ger. (Bruch) and Du. (broek) that have a sense of "marsh." In Sussex and Kent, it means "water-meadow," and in plural, "low, marshy ground."

In New England a brook is a decidedly flowing item. (Especially lately: Whetstone Brook, Brattleboro, Vermont, after hurricane Irene.)

~ Becky in Long Beach