I highly doubt it. There are several problems here. 1) You cannot violate the laws of physics (there is no process that is 100% efficient). You will never be able to completely eliminate the affects of friction and entropy.
2) Magnets have a force that is constant. This means that they cannot induce a movement of material or electrons unless the magnet also moves. This is similar to trying to use the force of gravity to create a perpetual motion device. Gravity is essentially constant as well and would require a change in strength to induce motion in an object.
However, I do believe that its possible to build highly efficient machines that rely on things like solar energy to work. One day you could built something that could run for year with no additional human input. However, it would eventually break down do to friction somewhere in the device or the natural processes of entropy.
To add to your magnet theory, take a look at an electric motor. There are plenty of magnets in it arranged in a circle. When electricity is applied to the coils, the shaft rotates. Its motion is continued because the coil that the electrons travel through is constantly changing.
A magnetic device like the image above would slow down down after it was started and eventually find an equilibrium point where it finally rests. There wouldn't be enough energy left in the system to carry on the motion
People have tried to make a machine like this for years, but no one has every succeeded. And even if you could make a perpetual motion device, as soon as you tried to make it expend energy to do some work, it would shut off. You can;t get more out of the system than you put into it.