We use different add-on based on our needs, but I think these are must have:
CTA Featured Threads
[bd] Widget Framework
Showcase
XenForo Media Gallery
XenForo Resource Manager
[bd] Banking
[bd] Paygates
Tickets
Advanced Application Forms
CometChat
Custom Tabs
Daily Digest
Weekly Digest
Email Idle Users
FAQ Manager
Font Awesome BbCode
Happy Birthday
Although I just use add-on that they are really useful, But if I want to say which one (just on or two) is my favorite add-on, then it will be "Showcase" and "CTA Featured Threads". Showcase is awesome.
The most useful add-ons (which are core to my site) are CTA Featured Threads, TMDb TV Thread Starter and TMDb Movie Thread Starter and anything by @Bob (Showcase which is an exceptional piece of work, Sportsbook, Stock Trader)
Personally, I have a soft spot for XFArcade...just because I like games and customizing stuff