If you want to a Java object as a serialized stream in java serialization format, then store it as a BLOB in the database.
But this is rather unusual, since it ties that column to java. If your database is, or may potentially be, used from another platform (like PHP), then store the object fields separately, mapping them meaningfully to regular SQL types.
There is no such thing as an object data type in a database. You could serialize the data as a string but I wouldn't recommend it since then searching or querying the object would be useless. Better to break the object up into meaningful, structured data.