Just about any part of the building envelope will leak if given the chance, but the places where leaks are most likely to occur are low and high on a building. Generally leaks occur where one material or part of an assembly meets another.

Basements and Band Joists
The area around the band joist has lots of potential for leaks because so many different materials come together here—the foundation wall, the mudsill, and wall and floor sheathing. The slab and the connection between foundation walls and slab also are potential leaky spots. Windows set in foundation walls are notoriously leaky.
Framed Walls
Gaps between sheathing panels, and the spaces between door and window jambs and the rough openings are typical places for air leaks. Pay particular attention to where exterior walls meet the foundation and the top plate. These are both spots where dissimilar materials meet and where barriers from one plane to another must be joined together.
Any through-the-wall penetrations also are a common source of leaks. This can include gaps around electrical service entrances, water and drain lines, vent hoods and any other spot where the barrier is breached.
Ceilings and Attics
Ceilings are full of opportunities for air leaks, not only around the perimeter, where ceilings meet walls, but also via the many penetrations that are common in the ceiling. They include recessed light fixtures, electrical and plumbing chases, gaps around chimneys, and holes for wiring, pipes and ductwork.
Air-Sealing Priorities
What to tackle first? Tests at an Owens-Corning research facility (summarized in the table below) provide a good idea of where you will get the biggest bang for your air-sealing buck.

These guidelines should be a starting point. The results may not translate to every house type or size, but they will get you started. Use a blower door to further hone your efforts.
For more air-sealing solutions, visit the JLC Field Guide.