It is normal that the hash is different each time. If you login you don't have to hash the password again.

I don't understand you. How can that be 'normal'. Isn't the whole reason about using a hash is that I save my password as a hash in my database instead of saving the real password, so that I can later hash the password I enter and compare it with the hash in the database?

It is normal. Laravel uses Bcrypt which uses random salts. The Hash process is one-way only, but Bcrypt will "unhash" it correctly to know if the passwords match :)

As already stated, the passwords are automatically salted with a random salt each new rehash.

You have a mistake in your code. You are rehasing password without checking if it's been hashed already. Try with

if(Hash::needsRehash($this->password))
	$this->password = Hash::make($this->password);

Okay.

if(Hash::needsRehash($this->password))
    $this->password = Hash::make($this->password);

This gives me an error, I only put in the hash when I create the account, I maybe didn't explain it enough.

It looks like this:

//Register a user;
	public function create()
	{
		if(Auth::check()) return Redirect::to('youraccount');
		
		$input = Input::all();
		$validation = Validator::make($input,User::$rules);
				
		if ( $validation->fails() ) {
			return Redirect::back()->withInput()->withErrors($validation->messages());			
		}else{
			$user = new User;
			$user->username = $input['username'];
			$user->fullname = $input['fullname'];
			$user->email = $input['email'];			
			$user->password = Hash::make($input['password']);
			$user->save();
			return View::make('youraccount')->with('input',$input);
		}
	}

	//Login a user:
	public function store()
	{		
		if(Auth::check()) return Redirect::to('youraccount');
		$authinput = Input::all();
		
		if (Auth::attempt(array('username' => $authinput['username'],'password' => $authinput['password'])))
		{
			return View::make('youraccount');			
		}		
		return Redirect::to('login')->with('message','Hmm, that probably was not the correct password');
		
	}

I only hash the password to save it when I create the account. I don't call the create() function again after that, so I never 'update' the hash in the database. If Auth::attempt is supposed to take care of everything else I am not sure what is wrong.