EE is coded such that searches are case insensitive.  However, your MySQL settings may result in some or all searches being done in a case sensitive manner.  This is most likely to occur with high-ascii values.

See this feature request where Paul explains that the best way to have high-ascii case insensitive searches is through your MySQL settings.  On MySQL versions 4.1 and above, setting your collation to match your language should resolve the issue.

It’s also possible for searches to be case sensitive if your MySQL collation setting is one that is by nature case insensitive, such as utf8_bin.