With VB4 we now have a couple options for you mobile users:
1. Mobile theme! If you log in with a mobile device, it should automatically select this theme for you, however you can always select it from the themes drop-down at the bottom left. Likewise, when logging in you can select 'Full Site' at the bottom of a mobile-theme'd page to get back to the normal theme for whatever reason.
2. Forum Runner app! This is a 3rd-party app which can browse the forum, and works with over 7k other sites. The app does cost you $1.99, but that's really a minimal expense in my opinion. It seems to work pretty well, and includes "most recent" pages, etc. It's also supported natively by vBulletin out of the box.
We've been asked if we'll support Tapatalk at some point, however at this time the answer is still no. It doesn't give anything that the other options have other than being $1.99 cheaper for users, however because it's a 3rd-party add on it requires additional overhead to maintain, and can trip up our systems updates if the plug-in isn't able to support newer vB software yet. For that reason we generally shy away from any additional modules unless they add something pretty significant to the experience.