Originally posted by Paul Sturrock:
... They are often "improperly" used in place of another pronoun in an attempt to convey a more formal or polite meaning...
Or ironically, in an attempt to be hypercorrect. This tends to happen when "me" is actually appropriate. They realize "I" isn't correct, but an aversion to using "me" causes them to opt for phrasing like, "Reply to Uma or myself."
(Meanwhile, my cat refers to himself as, "my own self.")