static_cast

static_cast is used for cases where you basically want to reverse an implicit conversion, with a few restrictions and additions. static_cast performs no runtime checks. This should be used if you know that you refer to an object of a specific type, and thus a check would be unnecessary. Example:

void func(void *data) {
  // Conversion from MyClass* -> void* is implicit
  MyClass *c = static_cast<MyClass*>(data);
  ...
}

int main() {
  MyClass c;
  start_thread(&func, &c)  // func(&c) will be called
      .join();
}

In this example, you know that you passed a MyClass object, and thus there isn't any need for a runtime check to ensure this.

dynamic_cast

dynamic_cast is useful when you don't know what the dynamic type of the object is. It returns a null pointer if the object referred to doesn't contain the type casted to as a base class (when you cast to a reference, a bad_cast exception is thrown in that case).

if (JumpStm *j = dynamic_cast<JumpStm*>(&stm)) {
  ...
} else if (ExprStm *e = dynamic_cast<ExprStm*>(&stm)) {
  ...
}

You cannot use dynamic_cast if you downcast (cast to a derived class) and the argument type is not polymorphic. For example, the following code is not valid, because Base doesn't contain any virtual function:

struct Base { };
struct Derived : Base { };
int main() {
  Derived d; Base *b = &d;
  dynamic_cast<Derived*>(b); // Invalid
}

An "up-cast" (cast to the base class) is always valid with both static_cast and dynamic_cast, and also without any cast, as an "up-cast" is an implicit conversion.

Regular Cast

These casts are also called C-style cast. A C-style cast is basically identical to trying out a range of sequences of C++ casts, and taking the first C++ cast that works, without ever considering dynamic_cast. Needless to say, this is much more powerful as it combines all of const_cast, static_cast and reinterpret_cast, but it's also unsafe, because it does not use dynamic_cast.

In addition, C-style casts not only allow you to do this, but they also allow you to safely cast to a private base-class, while the "equivalent" static_cast sequence would give you a compile-time error for that.

Some people prefer C-style casts because of their brevity. I use them for numeric casts only, and use the appropriate C++ casts when user defined types are involved, as they provide stricter checking.