The ‘oracle sqldeveloper’ stores all the connection details in an xml file ie. connections.xml.
If you want to have a backup for the connection details, you will have to navigate to
In windows XP
C:\Documents and Settings\<YourUserName>\Application Data\SQL Developer\systemX.X.X.X.X\o.jdeveloper.db.connection.X.X.X.X.X.X.X\
In Windows 7
C:\Users\<YourUserName>\AppData\Roaming\SQL Developer\systemX.X.X.X.X\o.jdeveloper.db.connection.X.X.X.X.X.X.X\
and take a backup of connections.xml .
Later, if you need to use the same connections on some other machine, you may simply copy the <Reference ...> tags for respective connections.