Orkut is basically a social networking service that is run by Google. It is very popular all around the world especially in Brazil and India. It was launched in January 2004 and currently has millions of users all around the world.
Your Orkut ID is based on your email account. So if you have forgotten your Orkut ID you can easily recall it with the help of the email address you used for it. You would most probably be using your Gmail account for Orkut so first check it out with that email ID.
If you still are not able to access it, go to Orkut homepage. Click on "I cannot access my account". Then click on " I forgot my user name". This would lead you to a step by step guide for the recovery of your email and password.
Hope it helps you out.