Middle English taken, from late Old English tacan "to grip, seize by force, lay hold of," from a Scandinavian source (such as Old Norse taka "take, grasp, lay hold," past tense tok, past participle tekinn; also compare Swedish ta, past participle tagit).
This is reconstructed to be from Proto-Germanic *takan- (source also of Middle Low German tacken, Middle Dutch taken, Gothic tekan "to touch"), from Germanic root *tak- "to take," which is of uncertain origin, perhaps originally meaning "to touch" [OED, 1989].
The weakened sense of "get to oneself, get in hand, obtain, receive, acquire" is by late 12c. As the principal verb for "to take," it gradually replaced Middle English nimen, from Old English niman, from the usual West Germanic verb, *nemanan (source of German nehmen, Dutch nemen; see nimble and compare nim).
OED calls take "one of the elemental words of the language;" take up alone has 55 varieties of meaning in that dictionary's 1989 edition. Already in Middle English one could take pity, charge, a nap, hostages, heed, the veil, fire, an answer, a concubine, a bath, pains, prisoners, place, possession, part, leave, advice, a breath, a spouse, a chance, comfort, flight, courage. Compare the range of senses in Latin capere "to take."
In the sense of "take effect, work," earliest in reference to transplants or grafts (mid-15c.). As "obtain (one's image) by drawing or painting" from c. 1600, hence the later use for photographic images. To take after "resemble" is from 1550s. Take that! accompanying a blow, etc., is by early 15c.
You can't take it with you (i.e. riches, to the grave) is the title of a popular Kaufman and Hart play from 1936; the idea in the quip is at least a century older. To take apart "dismantle" is by 1936.
To take five "go on a five-minute break" is by 1929, from the approximate time it takes to smoke a cigarette. Take it easy is recorded by 1880; the phrase take it or leave it is recorded from 1897. Colloquial figurative phrase what it takes "the right qualities" (for success) is by 1858.
To take it "absorb punishment" is by 1862; take the rap "accept (undeserved) punishment" is from 1930 (compare rap (n.)); take the fall in a similar sense is by 1942 (compare fall guy, by 1906).