What are some web based clients for GeoServer?

It depends on which services you want to provide/consume using Geoserver (WMS, WFS/WFS-T, or WCS). Based on the services you want to use, you can look for suitable clients. OpenLayers is one of the most advanced tools and documentation is good.

Other clients include:

• Mapstraction
• MapBuilder
• Mapbender
• GeoExt
• Mapfish

I would like to add:

• BruTile (Mapsui)
• SharpMap
• deegree

you might also consider openscales for flex/AIR based geoserver clients.