In OS X Mail.app (version 6.2 from OS X 10.8.2), I can see how to automatically add a signature for all new messages, but I do not want it automatically added when I reply to a message. Is there a way to achieve this?
Unfortunately, I do not believe this is possible in Mac Mail. I have been seeking a similar solution for a while, and I've yet to discover one.
There are ways you can make it a little easier to manually add and remove the signatures you want. For example, you can set your default signature to None, but then manually add your signature for all new emails. This preference is controlled under Mail > Preferences > Signatures. (To access this preference, you must select a mail account that the signature preference will be applied to in the leftmost pane. The box will not be clickable if All Signatures is chosen in the left pane.)
For me, this works acceptably - I reply to many more emails threads than I send new emails - but it may be different for your workflow.
Place signature above quoted text directly below the default signature selection box may also help. It doesn't remove the signature from the email entirely - instead, it separates the signature from the main body of your reply and appends it to the end of the email, after all quoted material. This will lead to many signatures all ganged up at the bottom of an email - one for each of your replies.
While the signature is still included in the message, choosing to place the signature after the quoted text may achieve the effect you are hoping for, as many email recipients will read all the way to the bottom of the quoted text in each reply to see the signature. It does not remove it entirely, however.
As you know, Outlook 2011 offers this feature on the Mac. I have heard that Mozilla Thunderbird supplies this functionality as well, but I cannot confirm that myself.