According to the American Heritage Dictionary of the English Language (Fourth Edition, 2000), an anniversary is:
It traces the etymology back to the Latin anniversarius, "returning yearly"; annus, year + versus, past participle of vertere, to turn.
In other words, an anniversary marks the passage of some number of years ("annually"). It is sufficient to say "first anniversary" or "fifth anniversary", and redundant to say "one-year anniversary" or "five-year anniversary".
Still worse is to specify a time interval other than a year, such as the currently popular abomination, the "N-month anniversary". A "three-month anniversary", for example, would mark the passage of three months of years (whatever that would mean), not three months. One may say instead something like:
Today marks the passage of three months since some event.or:
Nine months hence we will celebrate the first anniversary of something.
Some people have begun to use moniversary in such situations. While not yet widely accepted, it appears less defective than much other currently popular usage.
Call me annual-retentive.