A brief description of some of the Smalltalk implementations:
  GNU Project
The GNU Project has an open-source implementation of the Smalltalk-80 language which, unlike most other Smalltalk environments, is file based. GNU Smalltalk runs of course on GNU/Linux but also on most other POSIX type operating systems as well as Windows.

More info: gnu.org, smalltalk.gnu.org
  Pharo Project
The Pharo Project provides an open source - MIT licensed - Smalltalk-80 development environment for Windows, Mac and most Unix systems. The project provides a complete system including development tools and often used packages which is based on the small and stable Pharo core image.

More info: pharo-project.org, pharobyexample.org
Squeak is an open-source Smalltalk implementation created by a group which included some of the original Smalltalk-80 developers. Squeak is the vehicle for a wide range of projects from multimedia applications, educational platforms to commercial web application development.

More info: squeak.org, squeakbyexample.org
  Amber Smalltalk
Amber is an implementation of the Smalltalk-80 language. It is designed to make client-side development faster and easier. It allows developers to write client-side heavy web applications in Smalltalk. Amber includes an integrated development environment with a class browser, workspace, transcript, object inspector and debugger. Amber is written in itself, including the parser and compiler, and compiles into efficient JavaScript, mapping one-to-one with the JS equivalent.

More info: amber-lang.net
  Exept Software
Exept Software is a software company who have developed Smalltalk/X. Smalltalk/X is a free, complete implementation of the Smalltalk programming language.

More info: exept.de
  Gemtalk Systems
Gemtalk Systems is a software company that offers a number of Smalltalk products. GemStone/S is a proprietary Smalltalk object server for developing, deploying, and managing scalable, high-performance, multi-tier applications. GLASS (GemStone, Linux, Apache, Seaside & Smalltalk) which provides a way to create and deploy desktop-like web applications.

More info: gemtalksystems.com, seaside.gemtalksystems.com
Instantiations is a software company that provides the VA Smalltalk development environment. Instantiations have continued development of VA Smalltalk since 2005 when it acquired a worldwide license to IBM's VisualAge Smalltalk.

More info: instantiations.com
  Cincom Systems
Cincom Systems is a software company that offers 3 Smalltalk products as part of Cincom Smalltalk: ObjectStudio, VisualWorks and WebVelocity. ObjectStudio is a Windows-specific Smalltalk platform. VisualWorks is a cross-platform Smalltalk application development and delivery platform. WebVelocity is a browser based tool for building dynamic web applications.

More info: cincom.com, cincomsmalltalk.com
   Object Arts
Object Arts is a software company that provides Dolphin Smalltalk, a Windows specific Smalltalk implementation.

More info: object-arts.com
  Redline Smalltalk
Redline Smalltalk is a Smalltalk for the Java Virtual Machine.

More info: redline.st
  Smalltalk MT
Smalltalk MT is a high-performance, multithreaded implementation of the popular object-oriented Smalltalk language for the Windows platform. Smalltalk MT has a close integration with COM objects and fully compiled COM components can be created that operate in exactly the same way as C/C++ COM objects.

More info: objectconnect.com

Some interesting Smalltalk related implementations:
Self is a prototype-based dynamic object-oriented programming language, environment, and virtual machine centered around the principles of simplicity, uniformity, concreteness, and liveness. Self includes a programming language, a collection of objects defined in the Self language, and a programming environment built in Self for writing Self programs. The language and environment attempt to present objects to the programmer and user in as direct and physical a way as possible. The system uses the prototype-based style of object construction.

More info: selflanguage.org
Newspeak is a new programming language in the tradition of Self and Smalltalk. Newspeak is highly dynamic and reflective - but designed to support modularity and security. It supports both object-oriented and functional programming..

More info: newspeaklanguage.org
Lively is a new approach to web programming available as open source under the MIT license. Originally developed at Sun Microsystems Laboratories, it provides a complete platform for web applications, including dynamic graphics, network access, and development tools. Students, academics, and adventurous developers are encouraged to join the communitiy.

More info: lively-kernel.org
Clamato is an experimental Smalltalk dialect that is designed to operate within the JavaScript runtime. (For non-Canadians: “clamato” is what you get when you add clams to tomato juice. Some consider this an unholy mixture; others, a tasty treat.).

More info: clamato.net
Other implementations: #Smalltalk, Little Smalltalk, Panda SmalltalkSmalltalk YX, StrongTalk, ...