In terms of preference, our sites are designed & coded by hand. We find that we then have complete control over all aspects of the website we are creating, which helps keep the code much cleaner and easier to follow. It also minimizes the chances of easily avoidable mistakes which can be caused by more "automatic" HTML generators (such as certain visually-based interfaces and programmes).
We generally use EditPlus 2, or any other plain text editor to code our sites and various programs for creation and management of graphical content, such as Adobe Photoshop and Flash. For database creation and management, we generally use Microsoft Access.