I had a professor at my undergrad who would use an online service to create "mini-quizzes" throughout class; essentially, we would log into the service with our smartphones, he would place questions on his slides, and we would answer through the app/website. He could see the results live, and if enough people got something wrong he would go into more detail (this is very similar to the "iClickers" that some universities use).
I've seen some professors use Twitter as a means of enhancing the classroom - they would create a class account, and everyone would be expected to contribute by uploading photos, tweeting related news articles, and so on. I seem to recall this working best for classes in the natural sciences (biology, etc.) or fine arts (not that it couldn't be adapted for other fields, of course).
I also know of a professor at my undergrad who taught an interdisciplinary course that brought English majors, computer scientists, and a few others together to create a mobile application for a so-called "Poetry Walk" around the town. The group worked together to choose sites around town, create a piece of poetry associated with that site, and then build an app that would trigger a particular piece of poetry/spoken word based on your location.
Long story short - there's a lot of potential for mobile devices (I'm with scaaahu, if you're going to allow phones, why not allow tablets and laptops too?). It's really up to the instructor's imagination.
Based on O.R. Mapper's comment, I want to make a note that, for the foreseeable future, any activity in class that makes use of mobile devices should still not necessarily require students to have a mobile device. Simply put - this places students from less-fortunate (poorer) socioeconomic backgrounds at a major disadvantage, and it publicly reminds them of that.
The only exceptions I can think of are:
- A university such as my current one that requires all first-year students to have a laptop that meets at least certain specifications. In that case, asking students to bring their laptop is acceptable (though personally I think the requirement is a bit unfair, but that's my opinion).
- A course that requires the mobile device as a central piece of the course (i.e., the mobile app development course I mentioned earlier. Though development platforms - smartphones - were still provided by the instructor in that case).
Regardless - if having a mobile device is not a requirement for enrollment, as an instructor you have a responsibility to ensure that all students have the opportunity to participate equally in the activity.