When you send a preview email to yourself you will see only placeholders for any dynamically create links, such as: %unsubscribelink%%, %%webversion%% and %%Forward-to-friend%%.
In addition, any custom fields will not be filled in also. For example, if you have inserted the variables for First-Name and Last-name, the preview email might display the following salutation in the email:
Dear %%First-Name%% %%Last-Name%%, ...
This is because you are previewing the email and technically, there is no real data attached to this email. When the email is sent to your contact list, the links will be active, and all custom fields will be inserted.
You can add yourself to the contact list and send an email to yourself as a test, or maintain a separate list of contacts you send to for previewing.