More detail on Mr Dredel's answer and tuinstoel's comment. The data in the column will be stored in its specific case, but you can change your session's case-sensitivity for matching.
You can change either the session or the database to use linguistic or case insensitive searching. You can also set up indexes to use particular sort orders.
eg
ALTER SESSION SET NLS_SORT=BINARY_CI;
Once you start getting into non-english languages, with accents and so on, there's additional support for accent-insensitive. Some of the capabilities vary by version, so check out the Globablization document for your particular version of Oracle. The latest (11g) is here