"Tumble" and "topple" both bring to mind something falling down. But "tumble" makes me think of something rolling over and over, that kind of motion. I remember in physical education class we had to practice tumbling, which meant squatting down and placing our hands beside our heads and rolling over and over till we reached the end of the mat. A common children's nursery rhyme using "tumble": "Jack and Jill went up the hill To fetch a pail of water. Jack fell down and broke his crown, And Jill came tumbling after." "Topple" makes me think of a stack of books or boxes falling over when someone pushes from one side or when the stack becomes unbalanced because of improper stacking.

Simple is that: To tumble is to fall, as in Jack tumbled down the stairs. To topple is to push or throw over; overturn or overthrow

As intransitive verbs, "topple" and "tumble" share the meaning of falling down, but to truly tumble suggests end-over-end motion（筋斗）. If someone or something topples, then it just carries the idea of falling down or leaning toward falling.

Both words can mean to fall or to make something or someone fall. However, 'tumble' can also mean to move clumsily and/or hastily. "The four drunks tumbled out of the bar." 'Tumble' can also mean to roll around on the floor. "The boys tumbled with each other on the lawn, playing with each other."