Parameterless Constructors

If you're talking about generic constraints, yes:

class SomeContainer<T> where T : new() {
    ...
}

If you're talking about inheritance. It is not possible to require that every class that implements your interface or inherits your base class has a parameterless constructor.

The best you can do is use reflection in your base constructor to throw an exception (at runtime), like this:

abstract class MyBase {
    protected MyBase() {
        if (GetType().GetConstructor(Type.EmptyTypes) == null)
            throw new InvalidProgramException();
    }
}

If you're talking about a single class, yes; just put one in.