자주 means 'often' or 'frequently'. 자꾸 is similar in meaning but means something more like 'repeatedly' or 'over and over again'.자꾸만 is just an emphatic variant of 자꾸. 그녀는 나를 자주 괴롭힌다 -> She often bothers me. 그녀는 나를 자꾸 괴롭힌다 -> She keeps bothering me. The latter example has a much strong sense of constant repetition without ending.

I hear 자꾸만 a lot in lyrical contexts like song or poetry lyrics, so it arouses some deeper emotions. 자꾸만 보고 싶은 사람 a person who I want to see over and over again 자꾸만 눈물 나요. Tears keeps coming out (of my eyes). 자꾸 열받게 하지 마세요. Stop annoying me. 강아지가 자꾸 짖어요. The puppy keeps barking. 자꾸 넘어져요. I keep falling down.