Situation: You're building a new house
Solution: New construction window. This is the prime example of "new construction." There is no need to use replacement windows since you are not replacing anything.
Situation: You're building an addition
Solution: New construction window. This is just a smaller version of the previous situation. Unless there is some very out-of-the-ordinary circumstance (like you're incorporating a portion of an existing wall into your addition), you will almost certainly use a new construction window.
Situation: You're replacing a window whose framing is in very bad condition (rotted, termite-eaten, falling apart, etc.)
Solution: New construction window or replacement window. Because you will need to do a lot of carpentry work, it will be just as simple, easy, and cheap to install a new construction window as put in a replacement window. A new construction window certainly will be more substantial and provide better insulation from the elements than a replacement window.
Situation: You're replacing a window whose framing is in good condition
Solution: Replacement window. Installing a new construction window in a good wall will create more damage and work for you than a replacement window. This is because of the interconnectedness between the window, wall, wallboard, and trim.