Several people here have posted the same thoughts I have on redundancy. It really depends on where you are headed to and the expected odds, if you will, of needing redundancy.

When we go hiking locally near populated areas and on trails that see a lot of use, the kit and redundant items is much different then a kit I take for a multi day backpacking trip into the high country miles away from other people and immediate help (if any).

Nonetheless, there are critical items that are always redundant regardless of event, distance and number of people involved. For example, in my pack, amongst many other items, I carry a BIC lighter, large clear plastic contractors sized bag, small FAK, flashlight, Swedish Steel, Swiss Army Knife or multi-tool, compass. These critical and redundant items are also carried in my pants/jacket pockets or on my belt in the event I ever loose my pack. With these redundant items, my odds of survival have increased significantly.