ng-mouseover and leave to toggle item using mouse in angularjs

Angular solution

You can fix it like this:

$scope.hoverIn = function(){
    this.hoverEdit = true;
};

$scope.hoverOut = function(){
    this.hoverEdit = false;
};

Inside of ngMouseover (and similar) functions context is a current item scope, so this refers to the current child scope.

Also you need to put ngRepeat on li:

<ul>
    <li ng-repeat="task in tasks" ng-mouseover="hoverIn()" ng-mouseleave="hoverOut()">
        {{task.name}}
        <span ng-show="hoverEdit">
            <a>Edit</a>
        </span>
    </li>
</ul>

Demo

CSS solution

However, when possible try to do such things with CSS only, this would be the optimal solution and no JS required:

ul li span {display: none;}
ul li:hover span {display: inline;}

A little late here, but I've found this to be a common problem worth a custom directive to handle. Here's how that might look:

  .directive('toggleOnHover', function(){
    return {
      restrict: 'A',
      link: link
    };

    function link(scope, elem, attrs){
      elem.on('mouseenter', applyToggleExp);
      elem.on('mouseleave', applyToggleExp);

      function applyToggleExp(){
        scope.$apply(attrs.toggleOnHover);
      }
    }

  });

You can use it like this:

<li toggle-on-hover="editableProp = !editableProp">edit</li> 

I would simply make the assignment happen in the ng-mouseover and ng-mouseleave; no need to bother js file :)

<ul ng-repeat="task in tasks">
    <li ng-mouseover="hoverEdit = true" ng-mouseleave="hoverEdit = false">{{task.name}}</li>
    <span ng-show="hoverEdit"><a>Edit</a></span>
</ul>

I'd probably change your example to look like this:

<ul ng-repeat="task in tasks">
  <li ng-mouseover="enableEdit(task)" ng-mouseleave="disableEdit(task)">{{task.name}}</li>
  <span ng-show="task.editable"><a>Edit</a></span>
</ul>

//js
$scope.enableEdit = function(item){
  item.editable = true;
};

$scope.disableEdit = function(item){
  item.editable = false;
};

I know it's a subtle difference, but makes the domain a little less bound to UI actions. Mentally it makes it easier to think about an item being editable rather than having been moused over.

Example jsFiddle.