Who have been the doctors assistants in Doctor Who?

There have been many assistants within the show's run, and even more yet to come unless you only call the classic assistants "assistants". The first assistants, as you term them, may have been schoolteachers Ian and Barbara who traveled with the first Doctor and his granddaughter Susan. They helped bring out the Doctor's more compassionate side to include more than just his family and had influence on his preference for humans as his favorite alien species.

If this answer were to include the most recent companions, it would probably make it a bit dated in reference. However, the Doctor has aided and been aided by many, many allies and will continue to be as long as the show is still made.