When first trying to break compound words down in order to study and eventually stemmatize, they are often classified by what types of words make them up (i.e. noun, verb, adjective…). 

For example, in airport, there is the word air (noun), and the word port (noun).

Noun-Noun

Perspective differences cause it to be either a 4-6, or sometimes a debate between a 4-5. Without any context, something like earring will be a 4 because it is for the ear before it is on the ear.

Adjective-Noun

Adjective-Adjective

Preposition-Noun

The classification can also go further into things like verb-noun (i.e. fingerprinting) and verb-verb (freeze-dry, went & smoked)…

While searching for examples of compound words on the web, sites kept on referring back to the Wikipedia page on compounds in linguistics, and a more specific page on English compounds.

On the Wikipedia page, there is also what is called a Semantic Classification, where compounds fit into categories:

•endocentric: A+B denotes a special kind of B (ex. darkroom, smalltalk, doghouse)

consists of a head, i.e. the categorical part that contains the basic meaning of

the whole compound, and modifiers, which restrict this meaning

•exocentric: A+B denotes a special kind of an unexpressed semantic head

(ex. skinhead, paleface (head: 'person'), white-collar)

do not have a head, and their meaning often cannot be transparently guessed

from its constituent parts

•copulative: A+B denotes 'the sum' of what A and B denote

(ex. bittersweet)

compounds which have two semantic heads

•appositional: A and B provide different descriptions for the same referent

(ex. actor-director, maidservant, catfish)

lexemes that have two (contrary) attributes which classify the compound

For reference, Rick Walton has compiled a list of over 2000 compound words for teachers and librarians at:

http://www.rickwalton.com/curricul/compound.htm