How can I make the character follow the mouse pointer?

In the game I'm making, the character moves over a 2D plane in the 3D world (so y axis is never used for the character). I'd like to be able to control the character by making it follow the mouse pointer around but I'm having serious trouble getting this to work.

I'm guessing I have to find a way to combine the world and screen coordinates to a logical whole. Does anyone know how I can accomplish this?

Here's the gist of what I tried so far:

transform.position.x = Mathf.Lerp(transform.position.x, Input.mousePosition.x, 6*Time.deltaTime);

transform.position.z = Mathf.Lerp(transform.position.z, Input.mousePosition.y, 6*Time.deltaTime);

another option was:

transform.Translate(Input.mousePosition.x - transform.position.x , 0, 0);

transform.Translate(0, 0, Input.mousePosition.y - transform.position.z);

Which obviously isn't right...

Much thanks in advance!

See the LookAtMouse script proposed by capnbishop on the wiki :

http://www.unifycommunity.com/wiki/index.php?title=LookAtMouse

This makes the object smoothly rotate toward the mouse cursor. Then, you can translate the object forward. See the last instruction in the following code :

// LookAtMouse will cause an object to rotate toward the cursor, along the y axis.
//
// To use, drop on an object that should always look toward the mouse cursor.
// Change the speed value to alter how quickly the object rotates toward the mouse.

// speed is the rate at which the object will rotate
var speed = 4.0;

function Update () {
    // Generate a plane that intersects the transform's position with an upwards normal.
    var playerPlane = new Plane(Vector3.up, transform.position);

    // Generate a ray from the cursor position
    var ray = Camera.main.ScreenPointToRay (Input.mousePosition);

    // Determine the point where the cursor ray intersects the plane.
    // This will be the point that the object must look towards to be looking at the mouse.
    // Raycasting to a Plane object only gives us a distance, so we'll have to take the distance,
    //   then find the point along that ray that meets that distance.  This will be the point
    //   to look at.
    var hitdist = 0.0;
    // If the ray is parallel to the plane, Raycast will return false.
    if (playerPlane.Raycast (ray, hitdist)) {
        // Get the point along the ray that hits the calculated distance.
        var targetPoint = ray.GetPoint(hitdist);

        // Determine the target rotation.  This is the rotation if the transform looks at the target point.
        var targetRotation = Quaternion.LookRotation(targetPoint - transform.position);

        // Smoothly rotate towards the target point.
        transform.rotation = Quaternion.Slerp(transform.rotation, targetRotation, speed * Time.deltaTime);

        // Move the object forward.
        transform.position += transform.forward * speed * Time.deltaTime;

    }
}

This should be a valid base for what you intend to do.