I had a question posed to me about how to change the "Request new password" text on the User Login block, so I did a little investigation and came across a great article by Addison Berry of Lullabot that did basically what I wanted, but only to a different form. That, plus another article where she details her "Aha!" moments in Drupal theming really pulled the whole thing together and led to a fairly simple result.
The user_login_block function
The user_login_block function is part of the user.module and generates the form for us. This is separate from the individual login, register, and password pages found, just the "User Login" block, but can be easily extended to the others as well. In reading the definition of the user_login_block function, the last part to be added to the form is a section of links:



