Hello Everyone, 

At the time of this post, there are only two privacy settings from which you may choose when making a telephone call on the iPhone 3GS, to either show your outgoing Caller ID or to BLOCK/hide your outgoing Caller ID.  Which ever you choose, there is no officially supported method to override the selected setting for individual Contacts. 

For the record, I, like thousands of others, strongly urge Apple to address this particular white elephant that has taken up residence in the proverbial orchard.

To override iPhone 3GS Caller ID setting, do the following:  

NOTE 1
The following assumes that iPhone 3GS is set to BLOC/hide outgoing Caller ID.

NOTE 2
The following has been verified for the officially supported iPhone 3GS operating system, only.

NOTE 3
The following has been verified on the AT&T Wireless Network, only. 

1.
From the Contact List, select a Contact whom you wish to see your Caller ID.

2.
In the telephone number Edit Field, insert the prefix *31# before the telephone number.  For example, *31# (888) 555-1212

3.
Save the changes. 

NOTE 4
You may direct dial a telephone number using this prefix, as well.

NOTE 5
After adding the above listed prefix to a Contact telephone number, you will no longer be able to send a text message to that telephone number. 

NOTE 6
Since using a prefix in a Contact telephone number will prevent the Contact from being displayed during an incoming call, I suggest that you add an additional telephone number to the Contact mirroring the original telephone number but without the prefix.  For example:

Contact Name:  Mark
Mobile:  *31# (888) 555-1212
Other:  (888) 555-1212

This will allow the Contact to be displayed during an incoming call and provide a valid number to which you may send text messages. 

Mark