In an indirect way, the mitochondria work with pretty much every part of the cell. You've probably heard the mitochondria called the "powerhouse" of the cell, or some variant that indicates their importance in terms of energy generation. Nearly all of the functions of the cell, with some minor exceptions like osmosis, require the stored energy that the mitochondria produce.
In terms of specific organelles, the mitochondria tend to work alone, but they do have relationships with other cell structures. Their size and structure can have a direct impact on the availability of energy to their cell, so we might expect to find them in areas where lots of energy is needed. We also know that mitochondria have a close relationship with cytoskeletal structures, particularly microtubules, which may have an impact on their mobility as well as their function.
I think the most significant intracellular relationship that mitochondria have is actually with the nucleus. You may be aware that mitochondria have their own DNA, a remnant of the genome their ancestors carried when they were independent organisms. However, this genome is partially reduced, as some of the genes have been transferred to the nucleus. There are other species in which mitochondria have no DNA at all, having been entirely transferred. The significance of this, for the mitochondria, is that it is incapable of living independently, and now requires control from the nucleus in order to function.
The mitochondria, termed the "powerhouse" of the cell, works with other cellular organelles by providing them with the major form of energy know as adenosine triphosphate (ATP). ATP allows other cellular organelles to function properly maintaing the integrity of the cell. Mitochondria generates ATP through a process known as oxidative phosphorylation.
The mitochondria is the "powerhouse" of the cell. Its main job is to break down glucose into ATP (energy that the cell can use). The mitochondria does work with other cell organelles in that the ATP is dispersed throughout the cell to power the function of the cell. Specifically, the Ribosomes use the ATP to produce proteins in a process known as protein synthesis.