My understanding is that the SQL standard calls for case-insensitivity. I don't believe any databases follow the standard completely, though.
MySQL has a configuration setting as part of its "strict mode" (a grab bag of several settings that make MySQL more standards-compliant) for case sensitive or insensitive table names. Regardless of this setting, column names are still case-insensitive, although I think it affects how the column-names are displayed. I believe this setting is instance-wide, across all databases within the RDBMS instance, although I'm researching today to confirm this (and hoping the answer is no).
I like how Oracle handles this far better. In straight SQL, identifiers like table and column names are case insensitive. However, if for some reason you really desire to get explicit casing, you can enclose the identifier in double-quotes (which are quite different in Oracle SQL from the single-quotes used to enclose string data). So:
SELECT fieldName
FROM tableName;
will query fieldname from tablename, but
SELECT "fieldName"
FROM "tableName";
will query fieldName from tableName.
I'm pretty sure you could even use this mechanism to insert spaces or other non-standard characters into an identifier.
In this situation if for some reason you found explicitly-cased table and column names desirable it was available to you, but it was still something I would highly caution against.
My convention when I used Oracle on a daily basis was that in code I would put all Oracle SQL keywords in uppercase and all identifiers in lowercase. In documentation I would put all table and column names in uppercase. It was very convenient and readable to be able to do this (although sometimes a pain to type so many capitals in code -- I'm sure I could've found an editor feature to help, here).
In my opinion MySQL is particularly bad for differing about this on different platforms. We need to be able to dump databases on Windows and load them into UNIX, and doing so is a disaster if the installer on Windows forgot to put the RDBMS into case-sensitive mode. (To be fair, part of the reason this is a disaster is our coders made the bad decision, long ago, to rely on the case-sensitivity of MySQL on UNIX.) The people who wrote the Windows MySQL installer made it really convenient and Windows-like, and it was great to move toward giving people a checkbox to say "Would you like to turn on strict mode and make MySQL more standards-compliant?" But it is very convenient for MySQL to differ so signficantly from the standard, and then make matters worse by turning around and differing from its own de facto standard on different platforms. I'm sure that on differing Linux distributions this may be further compounded, as packagers for different distros probably have at times incorporated their own preferred MySQL configuration settings.
Here's another SO question that gets into discussing if case-sensitivity is desirable in an RDBMS.