Live until 120
The most often-cited source is Genesis 6:3.
In Deut. 34:7 the age of Moses upon his death is given as 120, but most importantly it says "his eye had not dimmed, and his vigor had not diminished."  To have one's mental and physical faculties—that is what we wish someone via "till 120." 
Although the blessing is quite appropriate, it is often used in ways that show it to be a part of every day conversation.
The number 120 even exists in humor, as in the story of a man who said to his noisy neighbor "May you live until 119" and then said to the wife "May you live until 120." When asked by the husband "why only until 119" the man who was seeking a bit of quiet said "she deserves one good year."
- Artscroll, p. 1123
- e.g. the title on http://www.ottmall.com/mj_ht_arch/v32/mj_v32i63.html#CRK
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