reticent / secretive / taciturn / laconic
One is reticent who is disposed to be silent, who has an inclination to keep his own counsel, is reserved, not inclined to speak freely.
Secretive means extremely reticent, having a disposition to secrecy. It is a stronger word than reticent and carries a slightly pejorative connotation. Reticence is often admirable; secrecy suggests furtiveness and implies there is something improper to be hidden.
Taciturn describes one who is habitually inclined to silence, reserved in speech, reticent in an uncheerful manner.
Laconic, unlike taciturn, is a rather laudatory term. It means using few words, being concise. (His political enemies considered Coolidge taciturn; his friends praised him for being laconic.)
from A Dictionary of Contemporary American Usage by Bergen Evans & Cornelia Evans (Random House, 8th printing, 1957)