gs's harshly downvoted answer is actually kinda right.
Standard SQL uses doubling to escape a literal apostrophe. MySQL's non-standard use of backslashes for escaping is the default setting, but it can be disabled and often is, in particular in sql_mode ANSI.
In this case only the doubled syntax will work, and any app you have using addslashes (or other ad-hoc escaping method) will break. mysql_real_escape_string will use whichever escaping method is best for the connection's sql_mode.
The multibyte encoding issue is also important if you're still using those nasty East Asian encodings that re-use the lower 128 characters, but then really you want to be using UTF-8 instead. \n-escaping, on the other hand, is of no concern since MySQL can perfectly happily cope with a raw newline in a statement.