c. 1200, "to watch with hostile intent, lie in wait for, plot against," from Anglo-French and Old North French waitier "to watch" (Old French gaitier "defend, watch out, be on one's guard; lie in wait for;" Modern French guetter), from Frankish *wahton or another Germanic source, from Proto-Germanic *waht- (source also of Dutch wacht "a watching," Old High German wahten, German wachten "to watch, to guard;" Old High German wahhon "to watch, be awake," Old English wacian "to be awake"), from PIE root *weg- "to be strong, be lively." General sense of "remain in some place" is from late 14c.; that of "to see to it that something occurs" is late 14c. Meaning "to stand by in attendance on" is late 14c.; specific sense of "serve as an attendant at a table" is from 1560s. Related: Waited; waiting.
To wait (something) out "endure a period of waiting" is recorded from 1849. Waiting room is attested from 1680s. Waiting list is recorded from 1841; the verb wait-list "to put (someone) on a waiting list" is recorded from 1960. Waiting game is recorded from 1835, originally in horse-racing.
When speed, not stoutness, is the best of a horse, quite a contrary system is practised. With such a horse, the jockey plays a waiting game; that is, he carefully nurses him through the race, so as not to distress him by overpacing him; as the finish approaches, he creeps up to his horses by degrees, but does not quit them to go in front till he sees that the pace has made them "safe," -- when he lets loose and wins. [James Christie Whyte, "History of the British Turf," London, 1840]