System.ValueType Understanding
ValueType is a little white lie.
The built-in numeric types (int, long, byte), char, enums and structs are all value types.
This means that they have a different concepts of identity and equivalence to object types. If I do x = y and x and y are reference types, then x and y now point to precisely the same object. However, if I do x = y and x and y are value types, then x and y are now two completely different objects that happen to be identical. (This is also reflected in == and Equals, though that can be overridden).
(This is where people get sidetracked by talking about the stack and the heap, if they haven't already, really that's an implementation detail and while important, is not the point of the distinction between value and reference types).
Now, mostly this is all and good but one thing about reference types is that they all benefit from inheriting from System.Object. The value type int doesn't really, and that's good too as it's much better in many ways that it just be four bytes of memory handled by the lovely CPU instructions that are so good at doing so. Still, it's sometimes useful to be able to treat an int as if it also inherited from System.Object, and so you can.
Of course, this means that you may do things with int that only make sense to do on a System.Object, so when you do so the int is "boxed" and can then be "unboxed" again.
This is great, but what if we wanted to do something specific to value types? More to the point, what if the designers of the CLR did (in particular, they wanted a GetHashCode for value types that related to the value-based equivalence descibed above, rather than the identity-based equivalence that objects have)?
For this purpose we have ValueType. The system treats all value types as inheriting from this class, which in turn inherits from Object. Enum in turn inherits from value type and all enum types inherit from it, allowing some common functionality across all enums.
So, if you ever want to treat a superclass of all value types, use ValueType, but if you want to actually create a value type, create a struct or an enum as appropriate.
The Common Type System explanation:
A structure is a value type that derives implicitly from System.ValueType, which in turn is derived from System.Object. A structure is very useful for representing values whose memory requirements are small, and for passing values as by-value parameters to methods that have strongly typed parameters. In the .NET Framework class library, all primitive data types (Boolean, Byte, Char, DateTime, Decimal, Double, Int16, Int32, Int64, SByte, Single, UInt16, UInt32, and UInt64) are defined as structures.
Like classes, structures define both data (the fields of the structure) and the operations that can be performed on that data (the methods of the structure). This means that you can call methods on structures, including the virtual methods defined on the System.Object and System.ValueType classes, and any methods defined on the value type itself. In other words, structures can have fields, properties, and events, as well as static and nonstatic methods. You can create instances of structures, pass them as parameters, store them as local variables, or store them in a field of another value type or reference type. Structures can also implement interfaces.
Value types also differ from classes in several respects. First, although they implicitly inherit from System.ValueType, they cannot directly inherit from any type. Similarly, all value types are sealed, which means that no other type can be derived from them. They also do not require constructors.
For each value type, the common language runtime supplies a corresponding boxed type, which is a class that has the same state and behavior as the value type. An instance of a value type is boxed when it is passed to a method that accepts a parameter of type System.Object. It is unboxed (that is, converted from an instance of a class back to an instance of a value type) when control returns from a method call that accepts a value type as a by-reference parameter. Some languages require that you use special syntax when the boxed type is required; others automatically use the boxed type when it is needed. When you define a value type, you are defining both the boxed and the unboxed type.
The strangeness of ValueType is to allow the above to happen.
Structures are value types. Value types are special because they are allocated on the stack rather than the heap. To "inherit" from ValueType, you must create a struct.
Not being able to derive from ValueType is specific to the C# compiler. If we look at managed C++ code:
value class Foo {};
value class Foo : System::ValueType {};
Both of these compile and are identical. Of course,
ref class Foo : System::ValueType {};
Will give error C3050: a ref class cannot inherit from 'System::ValueType'.
Not sure what other compilers allow.
If you want to derive from ValueType in C#, use struct and not class, and the compiler takes care of it.