From The Collaborative International Dictionary of English v.0.48:
Exist \Ex*ist"\, v. i. [imp. & p. p. Existed; p. pr. & vb. n. Existing.] [L. existere, exsistere, to step out or forth, emerge, appear, exist; ex out + sistere to cause to stand, to set, put, place, stand still, fr. stare to stand: cf. F. exister. See Stand.] 1. To be as a fact and not as a mode; to have an actual or real being, whether material or spiritual. [1913 Webster]
Who now, alas! no more is missed Than if he never did exist. --Swift. [1913 Webster]
To conceive the world . . . to have existed from eternity. --South. [1913 Webster]
2. To be manifest in any manner; to continue to be; as, great evils existed in his reign. [1913 Webster]
3. To live; to have life or the functions of vitality; as, men can not exist in water, nor fishes on land.
Syn: See Be. [1913 Webster]
From The Collaborative International Dictionary of English v.0.48:
existing \existing\ adj. 1. having existence or being or actuality; as, much of the beluga caviar existing in the world is found in the Soviet Union and Iran. Opposite of nonexistent. [Narrower terms: active, alive; extant, surviving] Also See: extant.
Syn: existent. [WordNet 1.5]
2. Present. Opposite of absent. [WordNet 1.5]
3. Presently existing; as, the existing system. [WordNet 1.5]