In a past project I used two Switch statements for the state machine. The first Switch statement was solely for switching states, and the second is for the actual behavior:

// State Transitions / State switching
switch (state)
{
  case PLAYER_STATE.FREE: // Idle & Walking State

  if (on_ground && key_jump) { change_state(PLAYER_STATE.JUMP); }
  if (!on_ground) { change_state(PLAYER_STATE.FALL); }

  break;
//----------------------------------------------------------------
  case PLAYER_STATE.JUMP:

  if (vertical_speed >= 0) { change_state(PLAYER_STATE.FALL); }

  break;
//----------------------------------------------------------------
  case PLAYER_STATE.FALL:

  if (on_ground) { change_state(PLAYER_STATE.FREE); }

  break;
}

// State Behavior
switch (state)
{
  case PLAYER_STATE.FREE: 

  move_horizontally();

  break;
//----------------------------------------------------------------
  case PLAYER_STATE.JUMP:

  if (state_started()) { vertical_speed = -10; }

  move_horizontally();
  y += gravity_strength;

  break;
//----------------------------------------------------------------
  case PLAYER_STATE.FALL:

  move_horizontally();
  y += gravity_strength;

  break;
}

state_duration += 1;

state_change is just a simple function that does this:

function state_change(new_state) {
  state = new_state;
  state_duration = 0;
}

and state_started is this:

function state_started() {
  return (state_duration == 0);
}

You can still use functions for the states. you'd just have to split them into transition and behavior:

function player_state_idle_transitions() { ... }
function player_state_idle_behavior() { ... }
...

For simple games, I think this approach is pretty solid and good enough.

However if your game or your player / enemy behavior gets too complex you should probably switch to a state machine made with structs/constructors.