I don't know which ones are supported the best, but I've used Larceny, DrScheme and Bigloo.
I believe that Larceny is widely believed to be the fastest open source scheme compiler available. It follows the unix tools based philosophy (no IDE). I don't believe it has 64 bit support yet. I haven't used it for a while, but the web site claims R6RS support. If I was to use scheme in anger, this is probably the system I would choose.
DrScheme is the one I use the most, because it's easier to use :) It has an IDE that understands the language as well as a profiler. It fits what I want from scheme quite well (ie playing around with things to find out how they work). It's performance has improved considerably since I started using it. Large set of libraries. R6RS support (mostly). 64 bit support for Linux.
Bigloo is interesting in that it targets several back ends, including JVM, .NET and native code.
All seem to have reasonable community support, but I see DrScheme mentioned the most.