A Unity MonoBehaviour that can be applied to a GameObject to provide simple turn on the spot joystick style player movement.

PlayerController.cs

using UnityEngine;
using System.Collections;

[RequireComponent (typeof(CharacterController))]
public class PlayerController : MonoBehaviour 
{
    /// <summary>
    /// The players character controller
    /// </summary>
    private CharacterController controller;

    /// <summary>
    /// The desired rotation of the player
    /// </summary>
    private Quaternion targetRotation;

    /// <summary>
    /// A float value used to set the speed of smoothed rotation
    /// </summary>
    public float RotationSpeed = 400f;

    /// <summary>
    /// A float value used to set the players walking speed.
    /// </summary>
    public float WalkSpeed = 2;

    /// <summary>
    /// A float value used to set the players running speed.
    /// </summary>
    public float RunSpeed = 6;

	void Start () 
    {
        // Set the reference to the character controller

        controller = GetComponent<CharacterController>();
	}
	
	void Update () 
    {
        // Get the input for both the horizontal and vertical axis. Use raw
        // to avoid acceleration.

        Vector3 input = 
            new Vector3(Input.GetAxisRaw("Horizontal"), 0, Input.GetAxisRaw("Vertical"));

        // If input is not equal to zero tell the character to look at the
        // input direction.

        if (input != Vector3.zero)
        {
            // Set the input direction

            targetRotation = Quaternion.LookRotation(input);

            // Smooth the rotation by multiplying vector Y by the
            // smoothed targetRotation Y. Smoothing is achieved 
            // via the MoveTowardsAngle function. This in turn is 
            // customisable using RotationSpeed

            transform.eulerAngles = Vector3.up * Mathf.MoveTowardsAngle(
                transform.eulerAngles.y, 
                targetRotation.eulerAngles.y, 
                RotationSpeed * Time.deltaTime
                );
        }

        // Create a temporary property to be used to calculate motion.
        // Initialy set motion to equal our input value.

        Vector3 motion = input;

        // Cater for angular velocity

        motion *= (Mathf.Abs(input.x) == 1 && (Mathf.Abs(input.z) == 1)) ? .7f : 1f;

        // Cater for run or walk. Multiply input dependant upon state.

        motion *= (Input.GetButton("Run")) ? RunSpeed : WalkSpeed;

        // Apply gravity

        motion += Vector3.up * -9.81f;

        // Move the controller

        controller.Move(motion * Time.deltaTime);
	}
}

// <copyright file="PlayerController.cs" company="dyadica.co.uk">
// Copyright (c) 2010, 2014 All Right Reserved, http://www.dyadica.co.uk
// This source is subject to the dyadica.co.uk Permissive License.
// Please see the http://www.dyadica.co.uk/permissive-license file for more information.
// All other rights reserved.
// THIS CODE AND INFORMATION ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY
// KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
// PARTICULAR PURPOSE.

// </copyright>
// <author>SJB</author>
// <email>contact via facebook.com/adropinthedigitalocean</email>
// <date>20.10.2014</date>
// <summary>A Unity MonoBehaviour that can be applied to a GameObject to provide
// simple turn on the spot joystick style player movement.
// </summary