Most list types in SharePoint 2013 natively provide the ability to find content within the current list.  As an example, I’ve created a custom list called “Countries” and you can see the search box here that allows me to filter or search for a specific country from within the list.  This is handy and prevents me from doing an actual “search” using the site search box and receiving all results related to one country from the entire search index.

Figure 1:  The in-list filter/search box of a custom list.
Figure 2:  Entering a term and seeing only results for that term
However, this capability is not available in every list type.  In fact, there are four list types that do not allow this natively.  For your reference, here are all of the list types broken down by those that do and do not allow in-list filtering/searching.
Allow in-list filtering/searching
  1. Announcements List
  2. Calendar List (“All Events” view)
  3. Contacts List
  4. Content and Structure Reports List
  5. Custom List
  6. Document Library
  7. Forms Library
  8. Issue Tracking List
  9. Links List
  10. Picture Library
  11. Promoted Links List (“All Promoted Links” view)
  12. Reusable Content List
  13. Site Assets Library
  14. Site Collection Documents Library
  15. Site Collection Images Library
  16. Site Pages Library
  17. Style Library
  18. Tasks List
  19. Workflow Tasks List
Do not allow in-list filtering/searching
  1. Discussion Board List
  2. MicroFeed List
  3. Survey List
  4. Wiki Pages Library
As a workaround, I recommend adding a filter/search web part to a custom page that would provide such functionality.
Update:  12/10/2013
It turns out that this is based on the default view of the list and its corresponding “Style” in some cases.  From what I’ve been able to determine, setting the style of a view to “Default” tends to bring back the in-list filter box.
  1. The default view of a Discussion Board is “Subject,” which doesn’t allow you to change the style.  However, a Discussion Board list comes with a view called “Management” that does include the in-list filter box by default.  Simply switch to that view and you’ll see it.  Of course, you can create your own custom view that includes the in-list filter box…just be sure the style of the view is “Default.”
  2. The default view of the Microfeed list is “All Items” and the style is “Default,” but it still does not include the in-list filter box.  I created my own standard view, ensured the style was “Default” and still had no in-list filter box.  In fact, I tried all of the styles for the Microfeed list.  The in-list filter box is just not available here.
  3. The default view of the Survey list is “Overview” and there is no link anywhere to create or modify views for the Survey list.  I did find that you can still get to the “Create View” page by manually navigating to “http://PasterYourSiteUrlHere/_layouts/15/ViewNew.aspx?List=PasteYourSurveyListGuidHere.”  I created my own standard view, ensure the style was “Default” and still had no in-list filter box.  In fact, my new view looked exactly like the default “Overview” view.  The in-list filter box is just not available here.
  4. The default view of the Wiki Page library is the “Home” page of the Wiki.  When you click on the library, it knows to bring up the home page instead of take you to the list of all pages.  You can easily get to the list of all pages that includes the in-list filter box by navigating to “http://PasteTheFullUrlOfYourWikiLibraryHere/Forms/AllPages.aspx.”  The style of this view is “Default” and looks as expected.