As cell phones have become commonplace, it has become accepted common courtesy to turn your ringer off or to vibrate during davening. Most Shuls strongly discourage talking on the cell during davening. Although some Shuls already have a no-digital-usage policy, many shuls have not yet established policies when it comes to less evasive digital usage.
With regard to reading and writing texts and emails, many Shuls allow it. The neighbor disturbance level is low enough, and many shuls are hesitant to prohibit behaviors which are not clear violations of the halacha. In the Shuls in my neighborhood, the texters are still a small minority, but in the event that a majority of people are texting in Shul on a regular basis, I think many Shuls will conclude that it is an inappropriate behavior and discourage it. Which makes you wonder why it’s not considered inappropriate now.
The next frontier is davening from IPads or other tablet computers. Since the IPad has a bigger screen which your neighbor can see, the potential for distraction is greater. As long as siddur and gemora viewing are the primary activities, most Shuls will probably not set a prohibitive policy. If people use the tablets for other things, I think minynan members will protest about the distraction and Shuls will discourage tablet usage, and perhaps cell phone usage as well.
We’re still early on the personal digital adoption life cycle and as the usage and frequency of usage evolves, it will be interesting to see how Shul policies change. It might make sense to get ahead of the curve and discuss and implement an appropriate digital policy for your Shul, since it’s harder to change behaviors when they’ve become entrenched.