Search through page titles? Is the Search module supposed to search through the node/page titles, or just the node content?

Because, for me it is only searching through the content, and not the page titles.

Note: I am using Drupal 7.
You didnt say what version of Drupal your using, but if you are using D6
check this out Views Search

If not then check out Views

Then I guess you just have to get the node titles and make them as a exposed filter.  So you will need to expose 1 Filter, one for the node title and then also check out Autocomplete Filter

This link can also help you Views Exposed Filter Search

Update : 

You might also wanna take a look on this, if your not to happy about using Views
, Its more integrated to the Search API
 Custom Search Module