Now with hundreds of apps in my device, it's really a pain to find an app. Sometimes I don't know its name, which makes it difficult to search. Is there a way to group the apps in my device? Somewhat similar to what we have in marketplace is fine.
Games are always grouped in the Games hub and don't appear in the app list. Otherwise, there is no official way to group apps except pinning them to Start. I've seen some people use live tiles/pinned web pages as titles for dividing categories on the Start page, that may be a workaround.
You can use an application such as New Group* to simulate groups on your start screen. It is not ideal, but is a reasonable workaround.
There is no way to organize the app list. But you do not need to:
If you have more than (I think) 40 apps installed, the same organization as in the People Hub kicks in; just tap a highlighted letter to easily jump to that part of the alphabet.
There is search button in the top left of the app list which searches for partial matches in all app names. It even has an option to search in Marketplace for apps you do not have installed yet, making it easy to find and download new apps right from there. Warning: this search button is new in Mango, so upgrade your phone if you do not see it.
Apps you use a lot, you can always pin to your home screen, which you can organize any which way you like.
You could use App Folder, sounds like it does what you want it to do.