GHC the Glasgow Haskell Compiler
GHC is an optimising compiler for Haskell, providing many language extensions. GHC is the defacto standard compiler if you want fast code. GHC is written in Haskell (plus extensions), and its size and complexity mean that it is less portable than Hugs, it runs more slowly, and it needs more memory. However, the programs it produces run much faster.
There is also an interactive environment, GHCi, which is like Hugs but supports interactive loading of compiled code. GHC provides profiling for time and space, and supports concurrent and (recently) parallel programming. It is available for most common platforms, including Windows, MacOS X, and several Unix variants (Linux, *BSD, Solaris).
The Haskell Interpreter Hugs
This small, portable Haskell interpreter written in C runs on almost any machine. Hugs is best used as a Haskell program development system: it boasts extremely fast compilation, supports incremental compilation, and has the convenience of an interactive interpreter (within which one can move from module to module to test different portions of a program). However, being an interpreter, it does not nearly match the run-time performance of, for example, GHC, nhc98, or HBC. It is certainly the best system for newcomers to learn Haskell. Hugs 98 is conformant with Haskell 98. Available for all Unix platforms including Linux, DOS, Windows 3.x, and Win 32 (Windows 95, Win32s, NT) and Macintoshs. It has many libraries including Win32 libraries, a foreign interface mechanism to facilitate interoperability with C and the Windows version has a graphical user interface, called WinHugs. Explanations of some common Hugs error messages and their causes can be found on Simon Thompson's page.
A small, easy to install, standards-compliant Haskell 98 compiler. It provides some advanced kinds of heap profiles not found in any other Haskell compiler. It produces medium-fast code, and compilation is itself quite fast. The compiler stresses the saving of space, that is, it produces small programs requiring comparatively little space at runtime (and it is itself much smaller than the other compilers). It is available for all Unix-like platforms (including MacOS-X, Cygwin/Windows, Linux, Solaris, *BSD, AIX, HP-UX, Ultrix, IRIX, etc.) - written in Haskell 98, but can be quickly and easily bootstrapped from C sources.
Yhc the York Haskell Compiler
HBI and HBC, Chalmers' Haskell Interpreter and Compiler
The Chalmers Haskell-B compiler 0.9999.5c implements Haskell 98, as well as some extensions. It is written by Lennart Augustsson, and based on the classic LML compiler by Augustsson and Johnsson. The interpreter can also load code compiled with HBC. There has been no official release for the last few years and the support level is pretty low, but the compiler exists and can be used. Unfortunately the web-pages and the documentation has not been updated the last few years! You can download an unofficial snapshot of the sources and the corresponding x86 Linux binaries (based on snapshots from Thomas Hallgren and Magnus Carlsson).
Helium is a functional programming language and a compiler designed especially for teaching Haskell. Quality of the error messages has been the main concern both in the choice of the language features and in the implementation of the compiler. The language is a subset of the Haskell language. The most notable difference with Haskell is the absence of overloading. The compiler keeps track of a lot of information to produce informative messages.
Jhc is an experimental compiler with a goal of testing new optimization methods and exploring the design space of haskell implementations.