About 8 years ago I switched from wearing "normal" shoes to wearing "minimalist" or "barefoot" shoes. They are thin soled, minimal cushion, flexible, zero drop (no slope from back to front), wide around the toes and lightweight. The basic idea is that your feet and ankles work amazingly well at absorbing impacts, adjusting to uneven surfaces, preventing sprains, etc if you let them do their job. If you put your feet in a supportive shoe, it works like a cast and your muscles atrophy. The shoe doesn't let them work like they should which causes knee pain, back pain, sprained ankles, and a host of other ailments. This also puts more stress on your other joints. Plus, most are narrow in the front which causes additional foot problems. Supposedly, we as a society have MUCH more trouble with foot injuries than people did prior to the invention of protective and supportive footwear.
As for my experience, I was relatively healthy (loved playing sports) but had frequent sprained ankles (1-3 per year), frequent knee pain, occasional back pain, pain in my Achilles tendon and foot pain if I was on my feet a long time. I was pretty sure I was going to rupture my Achilles at some point while playing sports. I switched to a pair of Merrell barefoot shoes and my issues slowly got better. As my body adjusted, most of those pains went away. I haven't sprained an ankle since switching, knee pain is basically gone (but quickly comes back if I have to wear supportive boots), back pain is greatly reduced, and my Achilles pain took about 6 months to go away. I do my best to wear nothing but minimalist shoes these days and am pretty successful. Steel toe boots at work are the biggest challenge.
Most of the barefoot/minimalist shoes are not cheap but many of them will tend to last a long time. There is no padding to wear down so there isn't really a need to replace them until they literally fall apart. I've bought most of mine on ebay or on sale. These days I primarily wear either Merrell Trail Gloves or Xero Shoes Prio. (The Xero Shoes come with a 5000 mile warranty on the sole and they are having a black Friday sale right now.)
If you do try these out, take it easy at first. It's easy to overdo it when using muscles that aren't used to being used. If you are a runner, start with small distances and work up to prevent injuries.