Things I find useful:
Tripod: Gitzo Levelling, very sturdy.
Camera: OM-D E-M1 Mk2 by Olympus Small, light, good resolution and great lenses. The worlds only f1.8 fisheye lens.
Panoramic Head: Adjustate by 360Precision Very good hardware, will last a lifetime. Sadly, they seem to have ceased trading, though there seems to be still some activity on social media. In my opinion there is nothing better engineered than their heads on the market at the moment.
Stitching: PTGui Pro Simply the best stitching software at the moment. Very powerful and flexible, yet another good support forum where panorama people hang out. Thanks to Joost for some great tips.
HDR Software: Photomatix Pro Excellent technical support and guidance on stitching HDR Panoramas, thanks Ron!
Panorama Creation: Pano2VR Very good software, being developed all the time to keep on the cutting edge. Great support through on a lively forum of users and support staff, thanks Hopki. Endless possibilities in designing your own skins to add to the user-interface.
Smartphone Stitching: I really like AutoStitch for smartphones from cloudburstresearch.com, it's really good for casual panos that aren't full spheres, still works fine on my phone, but is no longer downloadable. It has evolved into Google's own Street View app. This does things differently, but the end result is very similar. You can have a go at full 360 spheres, but it's a bit tricky to do this well.
Website Authoring: Rapidweaver Simple web authoring software to start with, but with lots of power and flexibility under the hood if you need it.
Reference: HDRI Handbook 2.0 Will tell you all you need to know about HDR photography.