Is it legal for a member function to say delete this?

A: As long as you're cautious, it's OK for an object to delete this.

Here's how I define "cautious":

You have to be absolutely 100% positive sure that this object was allocated through new (not through new[], nor through placement new, nor a local object on the stack, nor a member of another object nor a global,; but by plain ordinary new).

You have to be absolutely 100% positive ensure that your member function will be the last member function invoked on this object.

You have to be absolutely 100% positive ensure that the rest of your member function (after delete this line) doesn't touch any piece of this object (by including calling any other member functions or touching any data members).

You have to be absolutely 100% positive ensure that no one even touches the pointer itself after the delete this line. In other terms, you have to not examine this, compare this with another pointer, compare this with NULL, print this, cast this, do anything with this.

Of course the usual caveats apply in cases where your this pointer is a pointer to a base class while you don't have a virtual destructor.