Do any airplane designs exist that don't involve a flight surface that provides downforce? Most aircraft maintain longitudinal stability by balancing three forces:


The down force acting through the center of gravity (CG)
The lifting force acting through the center of lift
The down force acting through the center of pressure on the horizontal stabilizer.




My question is, what are some aircraft designs that deviate from this basic principle? Are there aircraft we see all the time that don't work this way? As a side note, how would weight and balance be affected if this principle isn't used?
There are multiple configurations which are possible with tail or canard, which based on their locations and whether they produce lift or down-force, results in a stable or unstable aircraft (taking the aircraft center of gravity into account). The figures below show some of the possible configurations.



Source: f-16.net

In the most general case, there is no need for even a canard or a horizontal tail as long as a (down or up) force is produced in some way. A good example is the Boeing Bird of Prey, where the chines produced (vortex) lift and thus a stabilizing force. The forces acting on the longitudinal axis of the aircraft look something like this, leading to a statically stable aircraft without any lifting surface except the wing.



Profile from bj-o23.deviantart.com, others own work.