My wife asked me about the etymology of the verb root in root for ‘support (a sports team)’; I looked it up in the American Heritage Dictionary and told her it was “possibly alteration of rout ‘to bellow, used of cattle.’” But I thought I’d better get a second opinion, so I checked the OED, which includes it in the entry for root “Of a pig: to turn up the ground, etc., with the snout in search of food,” updated September 2010, and says:
It has been suggested that it may be a transferred use of the sense ‘to dig’, ‘to turn up the ground’, perhaps ‘with the imagery of stamping so hard that one is visualized as digging a hole’ (see G. Cohen Stud. in Slang (1989) II. 67–8). A connection with rout v.4 ["Of cattle: to bellow; to low or moo loudly"] has also been suggested, but is unlikely on phonological grounds (although compare rout v.9) and also perhaps also on semantic grounds, since some early examples emphasize stamping and clapping rather than cheering.
The first citation is from 1889 (World (N.Y.) 7 June 11/4 “All during the game Jim never blinked, and he rooted more energetically and with twice the freedom of a Yorkshire porker”); the most recent gives me great pleasure:
2004 M. St. Amant Committed xx. 160 How can anyone root for the Yankees and claim to have a human soul?
Also under this root they include the Austral. and N.Z. coarse slang sense (‘fuck’), with the first citation from 1922, in (of all things) J. Joyce Ulysses iii. 719 (“All the poking and rooting and ploughing he had up in me”).