Common names are: ITU-T: tilde; squiggle; twiddle; not. Rare: approx; wiggle; swung dash; enyay; INTERCAL: sqiggle (sic).
Used as C's prefix bitwise negation operator; and in Unix csh, GNU Emacs, and elsewhere, to stand for the current user's home directory, or, when prefixed to a login name, for the given user's home directory.
The "swung dash" or "approximation" sign is not quite the same as tilde in typeset material but the ASCII tilde serves for both (compare angle brackets).
[Has anyone else heard this called "tidal" (as in wave)?]