Storing text inside a database, including things like blog posts, is something often done. There are database to handle this.
It's also common to store large content (eg images, large text files, etc) outside the database (ie in the filesystem) and reference them from the database. Doing this may limit your database size but presents other problems such as handling concurrency issues (like editing the file at the same time).
Lots of factors come into play to determine which is the most appropriate solution, including how often things are edited, how large the files are, how many files you have and so on.
As for database handling of text indexing, support varies. MySQL (using MyISAM storage) has full-text searching for example. SQL Server with the right add-on has it too. Same with Oracle. It can be useful but is more limited than a general-purpose search engine (eg Lucerne). Your requirements and constraints will determine if database indexing is sufficient or you need a search engine type solution.
To give you a real and specific example, the StackOverflow search is implemented using SQL Server full text searching and many have criticized it for being ineffective compared to using Google's "site:stackoverflow.com ...." (which I use by default pretty much).