Excessively submissive, obedient, or flattering.
Since he loves flattery, he surrounds himself with obsequious people, none of whom he ever really trusts.
A man may be obsequious toward his overbearing wife, or vice versa. Obsequious assistants are often called "yes-man" or "toadies" or even less complimentary things behind their backs. (Uriah Heep, in David Copperfield, is probably the most famous example in literature.) Obsequiousness has never been admired, but it has often been adopted as a good strategy.