Here's a list a put together a while back. It includes 3D and 2D engines.
3D Engines
Unity
Anyone making 2D or 3D games, simulations or visualizations can take advantage of Unity’s unrivalled toolset, efficient workflows and rapid iteration capabilities. With the uniquely versatile Unity engine, you can build anything from a 3D console title to a 2D mobile app.
Torque 3D
The Torque Game Engine, or TGE, is a 3D computer game engine originally developed by Dynamix for the 2001 first-person shooter Tribes 2. The current version is called Torque 3D. more >>
Blender
The Blender Game Engine is a component of Blender, a free and open-source comprehensive 3D production suite, used for making real-time interactive content. The game engine was written from scratch in C++ as a mostly independent component, and includes support for features such as Python scripting and OpenAL 3D sound. more>>
Unreal Development Kit(UDK)
In November 2009, Epic released a free version of UE3's SDK, called the Unreal Development Kit (UDK), that is available to the general public. According to the current EULA, game developers can sell their games by paying Epic the cost of $99 USD, and 25% royalty on UDK related revenue above US$50,000 from all UDK-based games or commercial applications. more>>
Unity 3D
Unity is a cross-platform game engine with a built-in IDE developed by Unity Technologies. It is used to develop video games for web plugins, desktop platforms, consoles and mobile devices. It grew from an OS X supported game development tool in 2005 to a multi-platform game engine. more>>
Ogre 3D
OGRE (Object-Oriented Graphics Rendering Engine) is a scene-oriented, real-time, flexible 3D rendering engine (as opposed to a game engine) written in C++ and designed to make it easier and intuitive for developers to produce applications utilizing hardware-accelerated 3D graphics. The class library abstracts the details of using the underlying system libraries like Direct3D and OpenGL and provides an interface based on world objects and other high level classes. more>>
Irrlicht Engine
An open source 3D engine written in C++. It is cross-platform, officially running on Windows, Mac OS X, Linux and Windows CE and due to its open nature ports to other systems are available, including FreeBSD, Xbox, PlayStation Portable, Raspberry Pi, SymbianOS, iPhone and Google Native Client. more>>
CryEngine 3 SDK
CRYENGINE SDK, originally called Sandbox Editor, is the current version of the level editor used to create levels for CryEngine by Crytek. Tools are also provided within the software to facilitate scripting, animation, and object creation. It has been included with various Crytek games (including, but not limited to, Crysis and Far Cry), and is used extensively for modding purposes. The editing style is that of the sandbox concept, with the emphasis on large terrains and a free style of mission programming. The editor can also construct indoor settings. more>>
Leadwerks
The Leadwerks Engine is a 3D game engine powered by OpenGL 2.1. It was designed by Leadwerks Software. Leadwerks Engine 2.0 made its debut in The Game Creators May Newsletter[1] on May 1, 2008. The engine makes use of the Newton Game Dynamics SDK 2.0 (Newton Archimedes) for physics, and OpenAL and EAX for sound and 3D sound effects. more>>
Neoaxis
NeoAxis 3D Engine is a free integrated development environment that allows for projects of all types and complexity. more>>
C4 Engine
The C4 Engine is a proprietary computer game engine developed by Terathon Software that is used to create 3D games and other types of interactive virtual simulations for PlayStation 4, PlayStation 3, Windows (XP and later), Mac OS X (versions 10.7 and later), and Linux. more>>
Shiva 3D
ShiVa3D is a 3D game engine with a graphical editor designed to create applications and video games for the Web, Consoles and Mobile devices. more>>
Panda 3D
Panda3D is a game engine, a framework for 3D rendering and game development for Python and C++ programs. Panda3D is Open Source and free for any purpose, including commercial ventures, thanks to its liberal license. more>>
Esenthel Engine
"Esenthel" is a mix of words: Essential and Essence. Esenthel Engine is a Next-Gen Computer Game Engine.
Supported Platforms: Windows, Mac, Linux, Android and iOS.
In development: Since Year 2000. Used by: Hundreds of Developers Worldwide. more>>
3D Game Studio
3D GameStudio or 3DGS is a pan 3D computer game development system which allows the users to create 3D games and other virtual reality applications, and publish them royalty-free. more>>
2D Engines
Game Maker Studio
GameMaker: Studio caters to entry-level novices and seasoned game development professionals equally, allowing them to create cross-platform games in record time and at a fraction of the cost!
Clickteam Fusion 2.5
Development software for creating video games, tools and apps.
Construct 2
A powerful ground breaking HTML5 game creator designed specifically for 2D games. It allows anyone to build games — no coding required!
Torque 2D
Torque 2D is an extremely powerful, flexible, and fast open source engine dedicated to 2D game development. more>>
Love 2D
LÖVE is a framework you can use to make 2D games in Lua. It's free, open-source, and works on Windows, Mac OS X and Linux.
RPG Maker VX Ace
RPG Maker VX Ace improves every aspect of RPG creation, making it not only the latest, but also the greatest engine in the RPG Maker Series. more>>
RPG Maker VX
RPG Maker VX allows you to make the roleplaying games you’ve always dreamed of by being one of the easiest game engine software ever developed. more>>
RPG Maker XP
RPG Maker™ XP gives you the power to create your own original RPG on Windows. Its popular and user-friendly interface has been carried over from RPG MAKER 2000. more>>
IG Maker
With IG Maker you have everything you need to create Platformers, Action RPGs, 2D Shooters or any combination of the three you can imagine! more>>
Dream Maker
BYOND is a free premier community for making and playing online multiplayer games. As a player, enjoy hundreds of games created by our community, by people just like you. As a developer, make your own indie sensation with an easy-to-learn language, built-in online support, tools for developers, and plenty of articles and tutorials.
Eclipse Origins
Eclipse Origins Silver & Gold (Aka EO 4.0) is the new official game engine of this site. It is an all-in-one game development suite that allows you to start up a client and server application and immediately begin creation your own 2D ORPG. more>>
M.U.G.E.N
M.U.G.E.N is a 2D fighting game engine that is enables you to create commercial-quality fighting games. Almost everything can be customized, from individual characters to stages, as well as the look and feel of the game.
Edward
A flash based platform engine.
Unity
Anyone making 2D or 3D games, simulations or visualizations can take advantage of Unity’s unrivalled toolset, efficient workflows and rapid iteration capabilities. With the uniquely versatile Unity engine, you can build anything from a 3D console title to a 2D mobile app.