These are used to count nouns and are placed after the numbers.  The  nearest equivalent in English would be something like "three head of  cattle".
가지 kinds, varieties, sorts
갑  pack (cigarettes), box
개 general counter; can be used if you don't know which 
specific counting word to employ
개월  month duration (Sino-Korean)
건         agenda items, assembly bills, incidents
곡 songs, music pieces
과 lessons, chapters
군데  places, institutions
권 books
그루 trees, rice plants, shrubs\
그릇/공기/접시  food (vessel, bowl, dish)
끼/끼니 meal
년  years (Sino-Korean)
다발 Bunch of flower
단 bunches/ bundles (radishes, scallions, wood, 
fruit)
달  month duration (Pure Korean)
달러, 센트   dollars, cents (English) (Sino-Korean 
counter)
대 vehicles (cars, airplanes) and 
machinery
대, 개비 tiny slender objects (cigarettes, matches, 
etc.)
대        injections, beatings
도 Degree (temperature) (Sino-Korean)
마디  phrases, joints, and musical measures
마리  animals
매 sheets of paper (formal/written form)
명 people (informal)
모 tofu, i.e. Block ,square, piece, cake
모금 a sip, a puff (water, cigarette)
문 artillery piece
벌  items of clothing, sets (chopsticks, dishes, documents, 
clothes, furniture, tools, cards)
병 bottles of liquid
봉지  paper bags
부  newspaper (or books if bought multiple copies) , printed 
copies (thesis, report, etc.), volume (of a book, magazine,etc.)
분 people (polite)
분 servings of food (Sino-Korean)
분  minute (Sino-Korean)
불, 전  dollars, cents (Sino-Korean)
사람 people (informal)
살/ 세  year (age)
상자  box, chest
손 two fish (typically mackerels or yellow croakers)
송이  picked flowers, bunches of grapes, bunches of bananas
숟갈, 젓갈  a bite, spoonful (rice, etc.)
시  hour (time. O'clock)
시간  hour (duration)
쌍         a couple, a pair (animate things)
알 eggs, pills, potatoes, candy
원  won (Sino-Korean)
월 month (of the year) (Sino-Korean)
일  day (Sino-Korean)
자루 things with long handles (writing instruments, shovels, 
swords, and rifles), and by extension, knives and pistols
잔/컵  cups, glasses
장 paper, sheets, leaf (flat objects such stamps, paper,  
        tickets, etc.)
점 pieces of art
접  one hundred dried persimmons
접시 main dish
줄 ten eggs
짝  one of a pair (ie. a shoe, a chopstick)
쪽 small slice (apple, garlic)"
채 house/buildings
척  boats and ships
첩 pack of herbal medicine
초  second (Sino-Korean)
층 floors (of a building Sino-Korean
?, layers
컬레  pair (gloves, socks, shoes)
코 twenty octopuses
타스 dozens of pencils
통 letters, telegrams, telephone calls, and e-mail, rolls of film, and also 
for buckets of water and watermelons
판 thirty eggs
포기 Chinese cabbages
푼 pennies
편         movies, poems, musicals
필 one animal (head of cow, horse, etc.), roll of cloth
해   years
회 exercise, writings, repetitions, innings, sorties, times, 
        rounds
original source at bonewso: