If you are using a connection pool this may be able to tell you. Oracle has various management views you ca use (e.g. v$session) which will tell you a lot about active connections. Have a look through the Administrators Guide.
Neither of these are programatic. But using Oracle's admin stuff
you should be able to find out if you are hitting the limit allowed and change that limit accordingly.
[ December 11, 2008: Message edited by: Paul Sturrock ]