A small example of using player states to handle movement.

Player.cs

using UnityEngine;
using System.Collections;

public class Player : MonoBehaviour {
  
	public enum PlayerState {MOVING_UP, MOVING_DOWN, MOVING_LEFT, MOVING_RIGHT};
	
	public PlayerState state;
	
	public float speed;
	// Use this for initialization
	void Start () {
		//must assign an initial state
		state = PlayerState.MOVING_RIGHT;
	}
	
	// Update is called once per frame
	void Update () {
		
		//Input only affects the state
		if(Input.GetKeyDown("up")) {
			if(state != PlayerState.MOVING_DOWN) {
				state = PlayerState.MOVING_UP;
			}
		} else if(Input.GetKeyDown("left")) {
			if(state != PlayerState.MOVING_RIGHT) {
				state = PlayerState.MOVING_LEFT;
			}
		} else if(Input.GetKeyDown("down")) {
			if(state != PlayerState.MOVING_UP) {
				state = PlayerState.MOVING_DOWN;
			}
		} else if(Input.GetKeyDown("right")) {
			if(state != PlayerState.MOVING_LEFT) {
				state = PlayerState.MOVING_RIGHT;
			}
		}
		
		//After Input, we decide what the player should do this frame, based on his state.
		switch(state) {
			case PlayerState.MOVING_LEFT:
				rigidbody.velocity = new Vector3(-speed,0,0);
				break;
			case PlayerState.MOVING_RIGHT:
				rigidbody.velocity = new Vector3(speed,0,0);
				break;
			case PlayerState.MOVING_UP:
				rigidbody.velocity = new Vector3(0,0,speed);
				break;
			case PlayerState.MOVING_DOWN:
				rigidbody.velocity = new Vector3(0,0,-speed);
				break;
		}
	}
}