NeXT was an active backer of Objective-C, and Apple inherited their interest in the language. The core OS X APIs all use Objective-C, and it’s the primary development language for OS X applications.
On the Free Software front, the GNUstep project has created a full implementation of most of the OpenStep specification—regarded by many as the unofficial standard library for Objective-C—as well as many Apple extensions.
Typically, the GNU implementation has lagged behind the NeXT/Apple implementation. The NeXT implementation supported Objective-C++—the mixing of Objective-C and C++ in the same source file—for some time before the GNU version added it.
While the dynamic dispatch of Objective-C makes it slightly slower than a static language such as C++, the extra flexibility is often worth the price. In an age when most desktop applications rarely use more than 10% of a modern CPU, it’s an increasingly attractive language for development.
Some features of Objective-C are just starting to appear in languages like Java and C#, usually with far less elegant syntax. Conversely, some features of new languages (Ruby in particular) are not present in Objective-C. With the release of Leopard, Apple intends to remedy this situation with a revamped Objective-C language: Objective-C 2.0.