http://libmemcached.org/ by Brian Aker, Commercial Support available from Data Differential
BSD license, it has been in production at websites for years. Aggressively optimised, ability to run async, supports binary protocol, triggers, replica, etc.
libmemcache
http://people.freebsd.org/~seanc/libmemcache by Sean Chittenden
BSD license. It is no longer under active development (last updated in 2006). You should try libmemcached instead.
apr_memcache
http://www.outoforder.cc/projects/libs/apr_memcache by Paul Querna
Apache Software License version 2.0 (doesn't appear to be actively maintained since 2005)
memcacheclient
http://code.jellycan.com/memcacheclient (cross-platform, but primary focus on Windows (last updated in 2008).
libketama
http://www.last.fm/user/RJ/journal/2007/04/10/rz_libketama (the original consistent hashing algorithm from last.fm)
PHP
Comparison of PECL/memcache and PECL/memcached
PECL/memcached
Io
http://github.com/iamaleksey/memcached-client-io/tree/master - libmemcached based CLI
libmemcached
http://libmemcached.org/ by Brian Aker, Commercial Support available from Data Differential
BSD licensed, contains a full set of CLI tools.
Protocol
To write a new client, check out the binary protocol docs and ascii protocol docs. Be aware that the most important part of the client is the hashing across multiple servers, based on the key, or an optional caller-provided hashing value. Feel free to join the mailing list for help and/or a link to your client from this site. Archive / Old
Danga Interactive list of clients http://www.danga.com/memcached/apis.bml
http://dealnews.com/developers/memcached.html - fastest client implementations (2006), obsoleted as more languages wrap the C-based libmemcached client library.