That's a great question! The rule book does not differentiate between a walk or a hit so a batter-baserunner can over run 1st on a walk.

Overrun first is all about intent. The batter/runner can be called out if he or she breaks to second or the umpire believes they have intent to to go to second. In baseball, coaches teach the batter/runner to turn away from the field or turn to their right. This is to show the umpire that they have no intent to run. However, that is not a rule and the runner could still be tagged out if and only if the umpire feels they have intent to advance.

Both responses above are correct. You may overrun 1st base on a walk or hit, and intent to proceed to 2nd base is what the umpires look for. HOWEVER, just to clarify John's note, there is no reason that the runner can not turn to the left. If BR does not display intent to go to 2nd, this is totally acceptable. Coaches teach the runners to turn right so as not to display any intent. However, many DO display intent on an overthrow at 1st, thus putting them in jeopardy at that moment.

Great answers! Yes, you may run through the bag at 1st on a walk. However, as the others stated, once you make a move toward 2nd, you're now "fair game" to tag out. Some girls get in trouble with this when we run way past first, then the ball gets by the 1b - some will see that and take a step toward 2nd and change their mind, but since they already made that move, they are in jeopardy and must get back to 1st or go to 2nd before they are tagged out. If they ran a good ways past 1st, they may very well find themselves in trouble.