Below is a comprehensive list of Chinese measure words and what they are used to count.

Hanzi	Pinyin	Use
把	bă	chair, knife, umbrella, toothbrush; objects with handles
包	bāo	pack of cigarettes; packets of objects
杯	bēi	tea, coffee, cup
本	bĕn	book, magazine
部	bù	film
串	chuàn	for items that come in bunches or clusters, e.g.: grapes or bananas
床	chuáng	blankets
顶	dĭng	hats
堵	dǔ	walls
对	duì	for items that are paired (but not necessarily so)
份	fèn	newspaper; share; portion; copies
封	fēng	letter (written document)
副	fù	sunglasses
个	gè	general measure word; people
根	gēn	bananas; other long, slender objects
罐	guàn	can (of soda or food); jar; tin
户	hù	homes; households
家	jiā	companies; buildings; households
架	jià	bridge; airplane
间	jiān	room
件	jiàn	clothes; luggage
届	jiè	events; used for events like the Olympics, World Cup, and such that occur frequently
斤	jīn	pound (actually 0.5 kilograms)
句	jù	phrase; remark
卷	juăn	reel; spool; toilet paper; camera film
棵	kē	tree
课	kè	text; lesson
口	kŏu	family members; household
块	kuài	soap; piece of land; Olympic medals; other things that come in hunks, chunks, or lumps; a measure of currency
辆	liàng	car; bicycle; wheeled vehicles
轮	lún	round (of talks, sports)
匹	pĭ	horses; bolt of cloth
瓶	píng	bottles
起	qĭ	cases (used for criminal case); batch, group (e.g.: visitors)
群	qún	crowd; group (of people); flock (of birds, sheep); swarm (bees); herd (animals)
首	shŏu	poems
双	shuāng	chopsticks; items that necessarily come in pairs
艘	sōu	boats; ships
台	tái	computers; televisions; radios; other machines
套	tào	set (of furniture, stamps)
条	tiáo	streets; rivers; fish; snakes; other long, winding objects
头	tóu	domestic animals; head of cattle; mules; other larger animals
位	wèi	person (polite usage)
张	zhāng	map; bed; table; other flat, rectangular objects
只	zhī	animal; one of a pair of body parts (hands, feet, ears); earrings; rings
枝	zhī	pencil, cigarette, pen; other long, thin objects
支	zhī	pencil, cigarette, pen; other long, thin objects
坐	zuò	mountains; bridges; buildings