While it's always dangerous to predict the future, particularly in an environment as fluid, dynamic, and evolutionary as web development, here are seven trends worth watching:
Convergence of design and development: Although there are still specialist front-end web developers, web designers, and back-end devs, all of these specific elements of web development are converging. It will still be possible and practical to specialize in one of these fields, but unless you're working for a very large company, you'll likely need to be sensitive to all three. Designers need to understand the needs of developers, and developers have a lot to learn about aesthetics and usability from designers. Both aspects of the user interface side of things need to acknowledge the importance of data in all forms of web development.
Applications, not documents: Web pages were a lot like documents in the early days, but that's simply not as true as it once was. Nearly every site out there now has some form of user interactivity on the front end, and some kind of data access on the back end. Visual appeal is extremely important, but you can't design a web page like a magazine page any more. A web page needs to do a lot more.
Finally some sensible standards: Since its birth, the web has always had compatibility problems. Most of the time there were several browsers with competing standards and capabilities. At times, one browser utterly dominated the landscape, making the other browsers irrelevant. Now for the first time in the history of the web, there are a set of standards (HTML5, CSS3, JavaScript) that are being adopted in a mostly universal way. This is a really huge deal, and it's about time. To reinforce this beautiful state, developers can do their part by using the standards and avoiding non-standard behaviors.
The web fits in a pocket and on the side of a building: For most of the history of the web, the desktop computer has been the unspoken standard. It's been possible to utilize the web on other devices, but they were always secondary to the standard desktop monitor, mouse and keyboard. Now all web development is mobile development. It's critical to design your sites so they can work on a variety of devices. Techniques like responsive design can go a long way here, but even that is not enough. Today's screens may be small, but they often have higher resolutions than the desktop machines of a few years ago. In addition, the demographics of web users are widening, so responsiveness to the needs of older adults and those with disabilities are increasingly important. The real lesson? You can't design for your own screen any more. You have to think about all the different kinds of devices and (much more important) people who will interact with your work.
Separation of display, content, and data: Any developer needs to understand display, content, and data to make them work together seamlessly. However, these elements must be separable. For example, visual trends come and go. (The web 2.0 aesthetic is gone. Flat design is hot this week; something else will come up next week.) It's critical to be able to modify one aspect without jeopardizing the others.
Use systems when you can: At the core, you'll always need to know how to do plain old HTML and CSS by hand. No matter whatever other tools you use, you'll always come back to these basic markup skills and the essentials of programming. However, this doesn't mean you shouldn't use tools to improve your efficiency. Most commercial web development today takes advantage of CMS systems, templates, and powerful tools like the jQuery UI toolkit. Learn and enjoy these tools, but never forget the fundamentals.
More technical can be more personal: Sure, the Internet is a highly technical beast. But it's at its best when it's used for the most human purposes: connecting people, sending a message, and making people smile. Although there are certainly technical and business applications of Web technology, perhaps the most exciting applications are the ones that people write as a form of personal expression. Maybe this crazy technical mumbo-jumbo is really a form of art after all.