From first glance, it would appear I have two basic choices for storing ZIP codes in a database table:
char(5) o
Normally you would use a non-numerical datatype such as a varchar which would allow for more zip code types. If you are dead set on only allowing 5 digit [XXXXX] or 9 digit [XXXXX-XXXX] zip codes, you could then use a char(5) or char(10), but I would not recommend it. Varchar is the safest and most sane choice.
Edit: It should also be noted that if you don't plan on doing numerical calculations on the field, you should not use a numerical data type. ZIP Code is a not a number in the sense that you add or subtract against it. It is just a string that happens to be made up typically of numbers, so you should refrain from using numerical data types for it.