With Drupal 7 there is now the search API. Apart from the existing database (that uses the same DB as drupal to index with) and Solr integration there are a few other backend options available too. As the open source community is quite prolific, a few supporting modules to allow fuzzy searching, multi index searching, saved searches, autocompletion, attachment indexing and more have sprung up. See the Search API project page for more detail.
Here's how we set up the database indexing: