When you share your contact data, you're giving others an easy and fast way to get in touch with you. In most cases, if you send someone what's called your vCard, a simple double-click will add you to his contacts list without the need for him to type anything in. It's really cool! To send someone your vCard, just pick up your card in Contacts and drop it on the Mail icon in the Dock.
You could also use Mountain Lion's fancy Share button, which is at the bottom of the Contacts window when you've got a card selected.
But what if some of the stuff you've got on your card isn't for public consumption? Your spouse's name, say, or your birthday? Well, you can configure your Contacts program so that it won't send what you don't want it to. To get started, go to Contacts> Preferences and click on the “vCard” tab.
As you can see in my screenshot, there's a box there labeled Enable private me card. Turn that on if it's not already, and then find whichever card your Mac thinks contains your information. You can look for the card with the silhouette next to it in your list…
…or you can choose Card> Go to My Card to jump directly there. (Incidentally, if Contacts thinks the wrong card is you, you can pick Card> Make this My Card with the right one selected to fix the problem.)
Next, click the Edit button to make changes to your card. When you do, you'll see a series of checkboxes appear on the right side.
So if you want recipients of your vCard to have your phone number and email address but not your physical address, all you've gotta do is toggle that checkbox off. Then, no matter how you share your card, that particular information won't be sent.
Ooooo, privacy. I know I sure don't want all of those crazy folks who get my card to know where I live. I should probably stop sending my vCard to crazy folks, shouldn't I?