Is "delete this" a bad idea?

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Is it safe to delete this?

I've been doing a little work on a class that's designed to act as a node in a linked list, and I figured I'd give the class its own deletion function as opposed to the managing class doing it. So basically it goes like this:

void Class::Delete() {
    //Some cleanup code before deleting the object
    delete this;
}

Now I've tested this and it appears to work fine, but I've had a problem in the past where objects have been in the middle of running code, been deleted, then obviously crashed the program by trying to use a no-longer-existing object.

Since "delete this" is right at the end of the function, it obviously exits the function and works fine, but is this sort of practice a bad idea at all? Could this ever blow up in my face if I'm not careful?