ArcGIS for Server can provide a number of Open Geospatial Consortium (OGC) web services (e.g. WMS, WFS, WFS-T, WMTS, WCS, WPS).
For a full list at ArcGIS 10.1 see this page.
Consequently, any Java client that can consume and work with these OGC services, can consume and work with services provided by ArcGIS for Server.
There is an ArcGIS Java web services API. It´s a SOAP SDK. You can download it for free even without having to sign in with your Esri account.
For a REST approach you can use ArcGIS Server endpoints (REST API). You only need a good JSON parser (e.g. Jackson).