>>> Can we place classes directly to appcode folder.

Yes you can. Absolutely. But using App_Code in production is not a good way. You should package by using Web Application Project (WAP). You can see great tutorial here :http://www.adefwebserver.com/DotNetNukeHELP/DNN4_WAP

>>> My requirement is, i need to implement some common functionalities in some modules.

Then you can make your own class as shared library. Your shared library class can be a single assembly or more after your recompile (it depends on your business process). And put it into your bin folder. Then your other module will freely to use that functionality. It's a better way then put your shared code inside App_Code folder.

HTH.