I am working in 2d. I need to accomplish a very simple thing. I have a prefab and I need to rotate it during the runtime in a direction where mouse pointer is. Basically I need this (black point is a mouse pointer):

When I move it up I want to accomplish this:
I created a simple script for that:
Vector3 position = Input.mousePosition;
position.z = this.transform.position.z;
this.objrigid.transform.rotation = Quaternion.FromToRotation(position, this.objrigid.position);
I was assuming that FromToRotation
will rotate object in direction from 1 point to another point, but it doesn’t really do that, object is randomly rotated when I move mouse, but in totally wrong directions. How would I accomplish this?
I use this script to make my player sprite look towards the mouse
Vector3 mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
transform.rotation = Quaternion.LookRotation(Vector3.forward, mousePos - transform.position);
Hope it’ll work for you. 
Hey Petrbena
Your mistake is a very common one! Input.mousePosition returns a Vector3 in screen co-ordinates, whereas Transform.position returns a Vector3 in world co-ordinates.
In order to convert the co-ordinates you will need to use a Camera:
http://docs.unity3d.com/ScriptReference/Camera.WorldToScreenPoint.html
I’ve made this script that gets a normalized Direction towards the mouse.
It does this based on your ViewPort, Just give it a shot and play around with it.
using UnityEngine;
using System.Collections;
public class NormMouse : MonoBehaviour {
public static NormMouse Instance;
void Awake() { Instance = this; }
Vector3 viewPortActual, viewPortDelta, directionToMouse;
/// <summary>
/// Retrieves a Normalized Vector3 Direction from mPosition towards the MousePos
/// </summary>
/// <returns>a Normalized Vector3 Direction from mPosition towards the MousePos (as WorldPos)</returns>
public Vector3 GetNormalizedDirectionToMouse()
{
// Calculate a direction based on the Mouse Position (using Viewport)
viewPortActual = Camera.main.ScreenToViewportPoint(Input.mousePosition);
viewPortDelta = new Vector3(0.5f, 0.5f, 0); // Detract Half the screen
directionToMouse = viewPortActual - viewPortDelta; // Caculate Direction
return directionToMouse.normalized; // Return normalized Direction
}
}
Here, I made another Class for you that looks at the position using my above code from afar 
Make sure the NormMouse script is somewhere in the scene, and there can be only one of them, because Singleton is applied 
using UnityEngine;
using System.Collections;
public class LookAtMouse : MonoBehaviour {
Transform mTransform;
void Start()
{
mTransform = transform;
}
// Update is called once per frame
void Update () {
mTransform.LookAt(mTransform.position + NormMouse.Instance.GetNormalizedDirectionToMouse());
}
I think that’s about the best explanation I can give you, but if you have any more questions, or need any details, fire away! If not, please accept this answer 
Best of luck ;3