Middleware for games is a piece of software that is integrated into a game engine to handle some specialized aspect of it, such as physics, graphics or networking.

Notable

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Autodesk Gameware - from Autodesk, includes Scaleform GFx, Kynapse, Beast and HumanIK
Nvidia GameWorks - visual FX, physics, particle and fluid simulations
Simplygon - automated 3D content optimization for a variety of assets as vegetation, buildings, scene views...
SpeedTree - vegetation programming and modelling software products
xaitment - customizable and modular game AI software for navigation mesh generation, pathfinding, character behavioral modeling and more

AI: Pathfinding, collisions

AiLive - a suite of game AI middleware
Kythera AI - Complete AI Toolset Middleware
Mercuna - 3D navigation middleware
Havok AI - Complete AI Toolset Middleware

Full-Motion Video

Bink Video - video file format, video compression tools and playback library from RAD Game Tools.
CRI-Sofdec - created by CRI Middleware. It is highly used in Dreamcast games.

Online Multiplayer

DemonWare - created by Activision.
Steamworks - used for Valve Corporation's Steam.

Physics & Animation

Cocos2D - 2D physics engine.
Euphoria - 3D human animation engine created by NaturalMotion based on Dynamic Motion Synthesis.
FaceFX - realistic facial animation engine created by OC3 Entertainment.
Havok - 3D physics engine.

Real-Time Rendering

trueSKY - real-time sky & weather renderer created by Simul Software.

Sound

CRI-ADX - created by CRI Middleware. It is highly used in Dreamcast games.
FMOD
Miles Sound System - audio authoring tools and engine developed by RAD Game Tools.
Wwise - audio engine and authoring tools from Audiokinetic.

UI

Gameface - UI middleware engine developed by Coherent Labs.