After reading your clarification comment, you have the option to utilize the siblings method in order to access the p elements that are siblings of the a elements. Assuming they have a common parent element, this code should suffice:
$('a.text_blue').click(function() {
$(this).siblings('p').removeAttr('class').addClass('blue_text');
});
If for some reason they are not actually siblings due to changes in the markup structure, you can use the parent method to navigate up to the div, and then employ the find method to target the descendant p elements:
$('a.text_blue').click(function() {
$(this).parent().find('p').removeAttr('class').addClass('blue_text');
});
In addition, there's an opportunity to refactor your code so that it doesn't require separate event handlers for each individual a element. One approach could be like this:
<a href="#" data-class="blue-text"></a>
Then, delegate the event handling as follows:
$(".color_changer").on("click", "a", function() {
$(this).parent().find("p").removeAttr("class").addClass($(this).data("class"));
});
Update
Now that you've shared a link to your code snippet, I'm able to provide a more specific solution! The p element you're aiming for is actually a sibling of the containing div:
$('a.text_blue').click(function() {
$(this).parent().siblings('p').removeAttr('class').addClass('blue_text');
});
Furthermore, with jQuery 1.6 at your disposal, you still have the advantage of event delegation using the delegate method:
$(".color_changer").delegate("a", "click", function() {
$(this).parent().siblings('p').removeAttr("class").addClass($(this).data("class"));
});