In your opinion what are must-have tools / resources for community managers?

My suggestions based on a lot of app discovery.

For Twitter monitoring use SocialBro with Twitonomy with influencer stats.

For Facebook and Twitter minute by minute monitoring there is HootSuite a market leader.

For Pinterest, I personally use Tailwind. 

For agencies for Fb,Tw, Ln and Pinterest I suggest Conversocial.

For live tweeting on the go use EveryPost app (iOS/Android)

For personal branding use Quora.

Monitoring and scheduling tools like hootsuite. It's the best way to stay organized and manage your channels in one window.