Is it common or good practice to have a table with only one column?

Common, no. But it isn't inherently bad practice - it is perfectly valid in principle.

What are you putting in the column?

Valid states for my app. For example, CA, NY, OR.

Just wondering if I should have an auto-incremented int ID column as well to serve as the primary key.

Apart from meaning your table now had two columns instead of one, what purpose would that ID column serve? Answer: none. The state code itself is unique and will serve as a perfectly good, natural, primary key. Stick with your one column - or perhaps more usefully, add a description column that tells the user that 'NY' means 'New York' etc.

I would convert that table into a multi-purpose table like so...

Code:

TABLE: Categories
Code        Value
---------  --------
MONTH     January
MONTH     February
  :            :
MONTH     November
MONTH     December
WEEKDAY  Sunday
WEEKDAY  Monday
  :            :
WEEKDAY  Saturday

Would you really? You don't care much about data integrity then! What stops the user inserting 'January', 'NY' or 'blue' into a "weekday" column?

This table would be considered a "setup" table.
So the dumb end-user (ex: data entry) would not be touching it.
Only a smart admin-user (ex: manager) would be playing with it.
Most likely the admin would set it up only once.
Ex: Add WEEKDAY and never add it again. Why? There are no more WEEKDAY!
Another Ex: There are only 50 STATES. Unless USA is acquiring Iraq as its 51'st state, then its safe to assume we only need to set the STATES up once.

But I wasn't referring to setting up the data in your "setup" table. I was referring to validating the data entered into all the other tables. Like this:

insert into customer (cust_id, state, delivery_day) values (1, 'december', 'green');

The concept I am alluding to is the foreign key. Your design precludes using foreign keys, and I don't like it!

I think that I'm probably genetically averse to the use of natural keys, but that aversion has come from experience... Things that "can't" change still seem to change on me, and at the worst possible times.

The population of California might decide to rename the state as "Ahnold-Stadt" and legislate the use of the abbreviation AS (they've actually done much weirder thing than that). This would cause great consternation, considering that Arkansas already used the state code of AS.

A natural key solution has no defense whatsoever against this kind of user-induced change. The problem is legislative, so there is no reasoning with it... You simply have to comply.

From a logical perspective, Tony has a good point and a natural key makes good sense. It still makes me nervous, since what is logical and what the real world requires are often two different things in my experience!

-PatP