Is there any API in which content can be ported from one CMS to another without creating any Package?
I have heard there is an API that exists on Tridion 2013 but could not find anything in Tridion 2011.
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The Import Export API was introduced in Tridion 2013 SP1. Previous versions have to make use of Content Porter. See also this documentation page (requires login)
You could use the Tridion Content Manager Core Service in Tridion 2011. This is a web service that will allow you access to the items within the CMS (provided that you have permission).
The Tridion 2011 SP1 documentation for the Core Service can be found in the online here: http://sdllivecontent.sdl.com/LiveContent/content/en-US/SDL_Tridion_2011_SPONE/concept_25F3C706E3A945A89870045A9ECAC139 (logon required)
However, if you do not need to do any manipulation to the content, then I'd strongly recommend that you use Content Porter - it provides a lot of additional functionality (exporting dependent content, etc.) that you will have to write yourself with a Core Service client.
You can also save the configuration used for Content Porter, and script the execution if you need to automate the process.
The Import Export API via the core service was added in 2013 SP1, so for earlier versions Content Porter is your best bet.
Even so, you can achieve pretty much the same results by saving a configuration file and running Content Porter from the command line. It's not immediately obvious how to do this, as the Click-Once install makes it a bit obscure to find the executable, but there are full instructions in the relevant documentation.