Short answer: no, it's making us smarter.

The long answer is by Nicholas Carr in The Atlantic (via Andrew Sullivan):

I can feel it, too. Over the past few years I’ve had an uncomfortable sense that someone, or something, has been tinkering with my brain, remapping the neural circuitry, reprogramming the memory. My mind isn’t going—so far as I can tell—but it’s changing. I’m not thinking the way I used to think. I can feel it most strongly when I’m reading. Immersing myself in a book or a lengthy article used to be easy. My mind would get caught up in the narrative or the turns of the argument, and I’d spend hours strolling through long stretches of prose. That’s rarely the case anymore. Now my concentration often starts to drift after two or three pages. I get fidgety, lose the thread, begin looking for something else to do. I feel as if I’m always dragging my wayward brain back to the text. The deep reading that used to come naturally has become a struggle.

What's destroying his attention span? Why, the internet of course.

Sigh.

He tells lots of anecdotes about his friends who say they just can't concentrate on text anymore. They can't read War and Peace like they used to. They've become power skimmers.

To which I say, if you don't like it, then don't do it. What's strange is that I'm finding an opposite effect in myself. While it's true that my tastes have changed (often books I enjoyed when I was younger just don't do it for me now), if anything my ability to focus has gotten better. In the past three years I've read as much for leisure as I always have. In addition, I've had to read textbooks, scholarly articles, and research-related books as well. Some of these are extremely long. Yes, I often skim for sections that are more relevant, but oftentimes I really do have to read every word, and I don't find my attention weakening. As I say, if anything I'm able to focus more intently and understand the content better.

Granted, I'm a single data point, but what if a rigorous study found that the internet really was changing reading habits and attention spans? My guess would be that in general it would be for the better. When it comes to information sources, having better skills to find relevant passages is a boon. In fiction, authors just have to work that much harder to keep readers hooked. What exactly is the downside?