Rise/fall and shift are the most useful architectural movements, but sometimes you need tilt and swing on both standards to get more rise/fall and shift than are built into the camera (indirect rise/fall/shift, as jnanian describes), presuming you have a lens that with enough coverage to use it. Dedicated wideangle cameras for architecture often have only rise/fall, and shift.
Shift is really useful for interiors, where you may want to do something like look straight down a hallway in the background on the right side of the frame, while showing a room in the, foreground that takes up most of the left side of the frame. Without shift, you either don't see the hallway (because the camera has to be too far to the left to capture the room in the foreground), or you move the camera right to capture the hallway and you lose the room on the left, or you use an ultrawide lens to get the room while looking down the hallway, and crop out everything right of the hallway, wasting part of the image and probably picking up some distortion from using a wider lens than would be ideal.