Hugin - A cross-platform open source panorama photo stitching and HDR merging program.
PTGui - Panoramic image stitching software for Windows and macOS.
Microsoft ICE - An advanced panoramic image stitcher created by the Microsoft Research Computational Photography Group.
Lightroom Photo Merge - Less control. Best for smaller panos.
Displaying Your Photos
GigaPan - Easiest way to host ultra-high resolution photos.
Prodibi - The prettiest and easiest solution. Best for embedding into websites or viewing fullscreen.
Zoomify - Easy all-in-one solution for creating and embedding zoomable images into websites.
OpenSeadragon - DIY solution; requires more work, but you have more control over the end result.