What is the legality of making a new game that is essentially the same as another, without using trademark names? For example if I make an obviously knockoff iOS game that is essentially something like Angry Birds? Can one patent games?
NOTE: Specific to the EU
Based on this:
Copyright will protect only the computer program in the form written by a programmer i.e. its source code. Neither the functionality of a computer program, nor the programming language or the format of data files used in a computer program in order to exploit certain of its functions constitute a form of expression of that program, and thus, those are not protected by copyright.
As such, you couldn't sell the direct source code, but you could make a derivative game with the same concept and execution, even in the same programming language, and sell it.
It's worth noting that creative works in the form of art are copyright-able, so you couldn't copy assets and if the assets were similar enough to the original game they might have a case against you. If in your Flappy Birds clone you made the bird a space ship and the pipes into asteroids then you'd likely have no problem.
Under US copyright law, claims have been made that the "look and feel" of a computer program is protected by copyright, particularly in Broderbund Software Inc. v. Unison World, Inc. That case established a broad protection for user interface elements of a program's design. More recent cases have narrowed this protection, and the extent of "look and feel" protection in US law is not currently clear. Non-US law may well be different, and the law on this point may change with future court cases.
As mentioned in another answer, specific artwork used in a computer game is protected by copyright, so any game using art based on the source (without permission) might be an infringement.
If you are planning to create or market such a "close" game in the US, you would be well advised to seek advice from a lawyer with experience in software copyrights, which is a sub-specialty of copyright law.