Old English creopan "to move the body near or along the ground as a reptile or insect does" (class II strong verb; past tense creap, past participle cropen), from Proto-Germanic *kreupanan (source also of Old Frisian kriapa, Middle Dutch crupen, Old Norse krjupa "to creep"), perhaps from a PIE root *g(e)r- "crooked" [Watkins].
From c. 1300 as "move secretly or to evade detection," also "move slowly, feebly, or timorously." In reference to imperceptible movements of things (soil, railway rails, etc.) from 1870s. Related: Crept; creeping.
1818, "a creeping motion, act of creeping," from creep (v.). Meaning "imperceptible motion" is by 1813 in reference to coal mines, 1889 in geology.
Meaning "despicable person" is by 1886, American English slang, perhaps from earlier sense of "a sneak" (1876). Creeper "a gilded rascal" is recorded from c. 1600, and the word also was used of certain classes of thieves, especially those who robbed customers in brothels. The creeps "a feeling of dread or revulsion" is first attested 1849, in Dickens.
Mission creep (1994) is American English, originally military, "unconscious expansion of troops' role in a foreign operation," and used especially in reference to the 1993 Battle of Mogadishu.
From the military perspective, the scapegoat for Somalia was "mission creep." We deployed for one discrete purpose and found ourselves employed for a multiplicity of other missions. This is naive. United States ground forces will likely never again deploy abroad without experiencing the demands of mission creep. [Ralph Peters, "Winning Against Warriors," in Strategic Review, summer 1996]