Webmention Implementations

Libraries

indieweb/mention-client-php - PHP library for sending webmention and pingpack notifications
indieweb/webmention-client-ruby - Ruby library for sending webmention notifications
phpish/webmention - Simple Webmention client (non-OO) in PHP packaged as a composer package
vrypan/webmention-tools - Python client library and command line webmention sender
pear2/Services_Linkback - PHP Pingback and Webmention client + server library
bear/ronkyuu - Python client library and command-line tools
glennjones/webmentions - Node.js a helper library for endpoint discovery, pulling validating Webmentions and sending Webmention requests
willnorris.com/go/webmention - Go client library and command-line tool for discovering and sending Webmentions.
webmentions-elixir - Elixir client library for sending Webmentions
Pushl - Command line client in Python for automating site-wide webmentions using a subscription feed (RSS/Atom/h-feed) for discovery

link_rel_parser - PHP http_rels($h) & head_http_rels($url) - HTTP header string parser for RFC5988 Link: rels (including X-Pingback) & function to curl a HEAD request and parse it all in one.
jgarber623/webmention-endpoint-ruby - Ruby client library for discovering Webmention endpoints
phpish/link_header - PHP Link header (RFC 5988) parser
PEAR: HTTP2 - PHP Link header (RFC 5988) parser (documentation)
ronkyuu - Python client library and command-line tools

microformats2 implementations and parsers
went - Webmention Endpoint Tools, a Python library that takes source and target URLs and does the rest of the job for you.

Some open source publishing software supports Webmention.

Known personal publishing software sends webmentions and accepts webmention comments (including webmention updates), and likes
FrancisCMS personal publishing software similarly sends and receives
WWWTech personal publishing software similarly sends and receives
phorkie sends and accepts webmentions to notify remote instances about forks

Some additional publishing software, portions of which are open source, supports webmentions:

Plugins exist for some open source publishing software

Webmention Rocks! is a Webmention validator which helps you debug your webmention sending. It will provide detailed error messages to help you successfully send a Webmention, and will show your comment on the website when it's successfully processed.
node-webmention-testpinger is a tool to ping your site with a variety of Webmention markup. Contains copies of a couple of real world examples of mentions that it enables you to ping locally to a development copy of your site.
node-webmention-testendpoint is tool to test your Webmention client. Generates a demo-post and a demo-endpoint to test if your client parses the webmention-endpoint correctly and to check if the ping body is transmitted correctly.
stapibas is a self-hosted service to send and receive Webmentions for websites and blogs. It can be used to send out Webmentions and Pingbacks for new posts on static sites.
A Firefox Add-On which allows you to send Webmentions via a context menu

brid.gy is a service that sends Webmentions for comments/replies, likes, and reposts on Facebook, Twitter, Google+, and Instagram posts. It uses original post discovery to find target links for the Webmentions. GitHub repo here.
Checkmention lets you test your Webmention implementation on your indieweb site, and whether it robustly detects certain types of XSS attacks. It also allows you to test for authorship spoofing.
mention-tech is a service that can receive Webmentions on behalf of anyone via both Webmention directly, and a web form on its home page.
webmention.herokuapp.com receives Webmentions for any registered page and allows them to be embedded through javascript.
webmention.io is an open-source project and hosted service for receiving Webmentions and Pingbacks on behalf of your IndieWeb site.
Telegraph is an open-source project and hosted service for sending Webmentions and Pingbacks.