C# and Java both derive from C and C++. Most significant features (e.g., garbage collection, hierarchical namespaces) are present in both. C# borrows some of the component concepts from JavaBeans (properties/attributes, events, etc.), adds some of its own (like metadata tags), but incorporates these features into the syntax differently.
Java runs on any platform with a Java VM. C# only runs in Windows for the foreseeable future.
C# is implicitly tied into the IL common language runtime (see below), and is run as just-in-time (JIT) compiled bytecodes or compiled entirely into native code. Java code runs as Java Virtual Machine (VT) bytecodes that are either interpreted in the VM or JIT compiled, or can be compiled entirely into native code.
Similar web components (e.g., based on JSP) not available in Java standard platform, some proprietary components available through Java IDEs, etc.
Win Forms and Web Forms RAD development supported through the MS Visual Studio IDE - no other IDE support announced at this writing. Swing support available in many Java IDEs and tools.
.NET common language runtime allows code in multiple languages to use a shared set of components, on Windows. Underlies nearly all of .NET framework (common components, ASP+, etc.).
Java's Virtual Machine spec allows Java bytecodes to run on any platform with a compliant JVM.
CORBA allows code in multiple languages to use a shared set of objects, on any platform with an ORB available. Not nearly as tightly integrated into J2EE framework.