With most database engines, you can execute queries manually at the
equivalent of a command-line. The database engine will show you
which indexes, if any,
it used when executing the query. Try this with some of your longer
running queries. You may be surprised at the results.
In some cases, even though various indexes may exist on a table, the
database engine may not be able to use them for your
particular type of query. Consider the pros and cons of
adding another index to this table.
As a general rule of thumb, try to create simple indexes (indexes on
just one field in a table). Simple indexes are often more useful
to the query engine than more complex, compound indexes. Additionally, the
simple indexes typically require less maintenance overhead for the
database engine used.