Rather than tailoring disconnected designs each tailored to a particular device or browser, we should treat them as facets of the same experience. In other words we can craft sites that are not only more flexible, but that can adapt to the media that renders them.
2012 was perhaps the year of the M-word (that's MOOC, in case you missed it) and open access, both of which captured the mainstream's attention for various reasons. This year it may be the turn of Responsive Design (or "I'm not saying native apps are dead but....").
I blogged about this idea some time ago, and I still hold a similar view. I think HTML5-based web apps will continue to grow at the expense of native mobile apps, as content providers realise that responsive design can often offer a far more elegant solution. Digital publishers must now now only consider downscaling desktop design for smartphones and tablets, but also upscaling it for TV. As HTML5 is accessible through any browser it means anyone can access it; with a native app you need an iOS version, an Android version, a Windows version (well, possibly :)).
Many people don't just use mobile devices to access content on the go, but more generally also. From a content provision perspective (particularly for publishers of journals, newspapers etc.) responsive design can work really well (The Boston Globe is one example, though they also have a mobile app alongside it, so make of that what you will!). In the context of library websites, evidence suggests a lot of people still view static information like opening hours and contact details from their phones. You don't need an app for that; good responsive design makes much more sense. However, the growing use of mobile devices does provide an opportunity to rethink your overall content strategy in general. Content providers normally pare down and streamline their information delivery significantly for mobiles, but if it's not important enough for the mobile environment, is it really valuable content at all? Delivering a more targeted and less cluttered content approach across all devices may well be a more successful way of reaching your users.
That said, there are obviously contexts where apps can add real value compared with simply viewing information in a browser. Content aimed at creating rich interactive experiences for users or apps that utilise functionality specific to certain devices (for instance, augmented reality apps that tourists can use on their phones) are some examples where native apps still make sense. Apps can also offer benefits from a branding and marketing point of view by creating unique and memorable experiences for the user, and this can apply for libraries also. So mobile apps may well be sticking around for the next while, but the nature and quantity of them may be very different to what we see today.