Yesterday I upgraded my iPhone 6S to 9.3. Today, I pulled out my phone in an attempt to show a client status on a Fedex delivery.

I clicked on the link in front of the CEO and Mail.App froze. After trying again and rebooting the phone, nothing worked. The meeting was derailed as we both realised that we were unable to click on links in Safari and Mail. His phone was broken as well!

Then I found hundreds of users posting the same issue to the Apple forums:

https://discussions.apple.com/thread/7505840?start=0&tstart=0

An unprecedented bug from Apple. I downloaded Firefox and could open links 50% of the time in a new tab. Chrome was unusable. Via the Apple forums I learned that a browser I'd never heard of (Puffin) seemed to work, and it did.

A few forum posts recommended deleting the Booking.Com app and resetting the phone. After more Googling I found that Ben Collier had likely identified what was happening here:

https://bencollier.net/2016/03/unable-to-open-links-in-safari-mail-or-messages-on-ios-9-3/

Ben's assertion was that "Universal Links", essentially a local database of URLS that automatically open Apps - was the likely culprit. Apparently Booking.Com had overloaded iOS by including several megabytes worth of URLs. This doesn't mean that other apps might haven't done this as well, and I'm not blaming Booking.Com here.

The upshot - be careful of upgrading to 9.3. Apparently Apple is working on a fix at present, this is rumoured to be delivered in a few days.