A growing number of clients are supporting WMS and WFS standards. These can all be used with GeoServer. The following list details some of the specifics on connecting to GeoServer. Please add any information and hints on using any of the following to connect to GeoServer. And don't hesitate to add additional clients (just click 'Add Child Page'), most GIS programs at least connect to WMS.
(could be good to have each child page comment on how what standards and versions are supported - perhaps a Template for clients?)

• ArcGIS — ArcGIS is the name of a group of Geographic Information System software product lines produced by ESRI. ArcGIS 8.3 and up includes support of OGC standards.
• ArcView GIS — ArcView GIS is a Geographic Information System software product produced by ESRI. ArcView GIS supports WMS as raster themes through ARC3WMS Extension by Refractions Research.
• BeeldBlad — BeeldBlad is an OGC Web Mapping Service 1. WMS client to be used in web pages. BeeldBlad (Dutch for "image sheet") is written in Adobe Flash and can therefore be used by all kind of browsers. It can be downloaded free of charge, so you can use it in your web mapping application.
• deegree iGeoportal — deegree's iGeoPortal client is based on OpenGeospatial Consortium's Web Map Context, which defines map client status information. Apart from benefits of using an open standard, the employment of the Web Map Context specification eases the development of clients by relying on reusable modules and making extensive use of XML technology.
• Drupal — Drupal is a content management system (CMS) that can be used to display WMS layers from GeoServer into Drupalized websites through Google Maps API
• Fulcrum — Fulcrum consists of several Swing/Java2d based well-developed client libraries.
• Geoar — Geoar is a GPL server side WebGIS client implemented in OpenLaszlo. Actually implements WMS service access (soon WFS).
• Google Earth
• Google Maps — OpenLayers is a free javascript mapping application that you can use to overlay maps from GeoServer on Google Maps, Virtual Earth, Yahoo! Maps, and other sources.
• gvSig — gvSIG is a desktop based tool for handling geographical information. It currently can connect to WMS, with WFS support coming soon.
• InterMap — InterMap is a portal based web map client, developed by UN-FAO and UN-WFP, focused on ease of use and low bandwidth situations.
• Internet Mapping Framework — IMF provides a powerful framework for quickly setting up mapping sites. It is closed source, supports WMS and WFS-T, and is J2EE java-based.
• MapBender — Mapbender is a GPL server side WebGIS client framework implemented in PHP. It is based on a user, WMS, WFS and GUI management and can be used as a framework to deploy geo portal software.
• MapBuilder — Mapbuilder is a LGPL client-side javascript library for putting mapping in a web page, using an AJAX style of interaction
• Mapserver — MapServer is an Open Source development environment for building spatially-enabled internet applications. It supports WMS, WFS and WFS-T (partially).
• Mobile Clients
• MyMaps — MyMaps is a java based open source WMS client
• NASA WorldWind — WorldWind is an amazing 3d viewer supported by NASA. It is an open source project, and it uses all standard WMS calls
• OpenJUMP — OpenJUMP is an open source GIS software written in Java. It is based on JUMP GIS by Vivid Solutions.
• OpenLayers — OpenLayers is a pure JavaScript library for displaying map data in most modern web browsers, with no server-side dependencies. It supports layers.
• PrimaGIS — PrimaGIS is a collaborative web mapping application for Plone. It is free software and licenced under the GNU General Public Licence (GPL).
• Quantum GIS — Quantum GIS (QGIS) is Qt based Open Source Geographic Information System built on top of GDAL and OGR.
• UDIG — User-friendly Desktop Internet GIS is an Eclipse-based desktop application supporting WFS, WMS and WFS-T protocols, put together by some GeoServer alumni working at Refractions Research.
• Virtual Earth — Virtual Earth is Microsoft's mapping solution, both 2d and 3d, all online.
• worldKit — worldKit is an easy to use and flexible mapping application for the Web. Light weight GIS. It's a SWF based app, configured by XML, data fed by RSS. It support WMS.

These can be roughly divided along four axes, desktop vs. web-based and open source vs. closed source. Recently there is also the wildcard 3-D viewer axis, with NASA WorldWind and Google Earth, both free to download, WorldWind is open source.

Open Source Desktop

QGIS, gvSig, and uDig are all open source desktop GIS's that can connect to web services. uDig is currently the most advanced on that front, connecting to WMS and WFS, as well as allowing editing through WFS-T. gvSig has WMS, and should have WFS support in their next release, and QGIS supposedly has partially implemented WMS. Each offers various strengths and weaknesses. Our favorite is uDig, though we're biased, since it's built on the same great GeoTools toolkit that GeoServer is.

Closed Source Desktop

Right now we just have ArcGIS listed on the closed source side, though there are many others - connecting to WMS is becoming a standard feature of any decent desktop GIS.

Open Source Web-based

MapBuilder is our pick for a web-based client, though it is more of a toolkit than a framework. It supports WMS and WFS-T. For a fuller framework check out MapBender or PrimaGIS - both are investigating using MapBuilder's javascript functionality on top of their framework base. MapBender has better WFS support, but PrimaGIS uses the very nice Plone framework. InterMap is a good option for those who have low bandwidth situations - it composes the image on the server side, instead of sending each layer down to clients. It only supports WMS, but can also connect to ArcIMS. The next version should incorporate javascript functionality to be more useable.

Another option is the deegree iGeoportal web-based client. The deegree iGeoPortal is able to handle layers from more than one WMS and offeres the opportunity to store the current state of the client in a Web Map Context compliant XML document.

Closed Source Web-Based

IMF is our favorite closed source web-based framework, it is used for our User Map.