Yes, you can delete a Topic/Discussion you have posted if there have been no replies directly to your message.
To delete a new topic, click on the Remove Thread link in the Actions panel to the right ofthe message.
To delete a reply to a topic, click on the Delete link at the bottom of the reply.
Once someone else has replied directly* to your message the Delete option goes away.
*If there are replies posted to other messages in the thread, even if posted after your reply, you will still be able to edit/delete. It is when someone replies directly to your message by clicking the Reply link on your message that the ability to edit/delete goes away. Any replies to any messages in a thread will remove the edit/delete options from the initial message.