Red5 only contains a server-implementation (in java).
The python project rtmpy aims to be a free software implementation of an RTMP library, whilst Tape intends to be a full streaming server (in Python). rtmpy is in active development.
There is a java client implementation of RTMP, called Flazr. As of 2nd June 2009 (just two weeks after Adobe issued the take-down notice), Flazr also has RTMPE support. Congratulations to Peter, and thank you to Adobe: none of this would have remotely happened, if you hadn‘t brought RTMPE to people‘s attention.
SWFDec has a partial and experimental implementation of RTMP. swfdec is client-only.
Gnash has a partial and experimental implementations of RTMP. Gnash has both client and server, sharing the same common source. Cygnal is making particularly good progress, as a server: video can already be streamed from it, with real-time video planned for Q3 2009.
libRTMP by boxee contains an RTMP client library, and was used as the basis for rtmpdump.
haxeVideo is a server implementation of RTMP in Haxe.
crtmpserver is a server implementation of RTMP that has implemented (as of 25th may 2009) the RTMPE protocol.