The short answer is- nothing. Perfectly good recordings have been made entirely with computer plug-ins and a DAW. However, if you intend to use outboard gear, I think the essentials are:
A good 2 channel mic preamp (add as many simultanious channels as you need)
A reverb unit or multi-FX box
A power conditioner
A compressor
An EQ unit
A Headphone distribution amp
Optional:
A noise gate
A guitar amp modeler
A Bass amp modeler
Absolutely essential:
A lava lamp-Richie