Indo-European
The most well known of all language families is the Indo-European, which comprises roughly 12 major groups and hundreds of languages. The major groups or subfamilies are Celtic, Italic (including Romance), Baltic, Slavic, Germanic, Anatolian, Greek, Indic, Iranian, Tocharian, Albanian, and Armenian. In addition, it appears that Baltic and Slavic should form a larger Balto-Slavic group, and Indic and Iranian should be placed in an Indo-Iranian group.
Here's small list of words common to most Indo-European languages:
 

Group	Language	Lexicon
		"father"	"mother"	"brother"	"two"	"three"	"four"	"horse"
Germanic	Old English	fæder	modor	broðor	twa	thrie	feowre	eoh
Italic	Latin	pater	mater	frater	duos	tres	quattuor	equus
Celtic	Old Irish	athair	mathair	brathir	do	tri	ceathair	ech
Hellenic	Greek	pater	meter	phrater 1	duos	tri	tetra	hippos
Indic	Sanskrit	pitar	matar	bhratar	dva	trayas	chatvari	asva
Iranian	Avestan	pitar	matar	bratar	dwa	trayo	chatvaro	aspa
Slavic	Russian	otech	matka	brat	dva	tri	chetyre	loshaa (kon)
Armenian	Armenian	hayr			erku	erek'	cork'
Tocharian	Tocharian B	pacer	macer	procer	wi	trai	s'twer	yakwe
Proto-Indo-European		*pəter	*mater	*bhrater	*duwos	*treyes	*kwetores	*ek'wos

Note:
1. Greek phrater means "clan member"
Sino-Tibetan
Another large language family is the Sino-Tibetan, including Sinitic (all forms of Chinese) on one main branch and Tibeto-Burman (Tibetan, Burmese, and thousands of others) on the other main branch.
In the following example tones are omitted so that I have less work to do :)  Also, note that I threw out Pinyin transliteration for Mandarin and used something of my own that also works for other dialects: /ś/ corresponds to voiceless palatal fricative (/x/ in Pinyin) much like /ch/ in German ich; /x/ is the voiceless velar fricative like /ch/ in Scottish loch; /ə/ is the central vowel schwa; /ʔ/ is the glottal stop; and /C/ means any stop consonant.
 

Group	Language	Lexicon
		"I", "me"	"two"	"three"	"six"	"name"	"eye"	"blood"
Sinitic	Mandarin	wo	er	san	liu	ming	mu	śie
Sinitic	Yue	ngo	yi	saam	luk	ming	muk	hüt
Sinitic	Wu	ngu	liã	se	loʔ	ming	moʔ	śiʔ
Sinitic	Middle Chinese	nguo	ñi	sam	lyuk	myeng	muk	xwiet
Sinitic	Old Chinese	nguo	niys	səm	C-ruk	myeng	myək	swi:t
TB	Tibetan	nga	gñis	gsum	drug	ming	myak	yi (1)
TB	Burmese	nga	hnats	sum	khrok	ə-mañ	mig	swiyh
TB	Kachin	ngai	ñi	məsum	kruʔ	mying	myiʔ	sai
TB	Lepcha	ka	nyi	sam	ta-rak	ming	mik	vi