The best introduction to programming professionalism that I know of is a book called The Pragmatic Programmer. It discusses various aspects of software development, and is useful to learn what you don't know. It's also small and easy to digest compared to a more complete (hur hur hur) book like Code Complete.
For web development, your next step is to learn about the Model-View-Controller pattern. Building a small project using a framework like Yii, or CodeIgniter should allow you to get the hang of it.
The most important idea behind MVC is separation of concerns. If you separate your code well, then changes to one part of a program won't affect other parts negatively.
Your code will spend about 80% of it's lifetime in maintenance mode. That's when you have to go back to fix bugs or add new features. After a year, you won't remember what you coded any more. (I don't remember what I coded last month.) The more readable and well-structured your code is, the better for future you. Code readability is very important.
Documenting your project is important too! You don't want to try to remember what the database password used to be. Keep login and hosting details down in a secure location.
Finally, learning new languages (plural!) will help you become a better programmer. I like Python, so I suggest you start with that.
Also, if you are so inclined, the Tao of the Hacker may prove enlightening.
UPDATE 2018: Since this question was asked, several options for self-taught developers to get a more formal education have opened up. I still think the books above are a great foundation for programming craft, but the study plans mentioned below can help you get really solid technical skills.