I was making cranberry chutney, and cooked it slightly too fast (thank you, electric stove!)
Result: the chutney is fine, but there’s a charcoal coating of burnt sugar on the bottom of the pan. I’ve tried soaking it, and some of it has come off, but not all.
How can I get the rest off?
Put a fabric softener sheet in the pan and add warm water. Let it soak for a few hours and it’ll rub right off. I’ve only used the sheets, but this may work with liquid softener as well.
It depends on the type of pan, but here’s one option to try:
Sprinkle with a few tablespoons of baking soda, add water, and bring to a boil. Then let it sit for a few of hours.
Another option that I’ve heard, but never tried, is using hydrogen peroxide in place of baking soda.
I go with straight bleach, overnight.
I’ve found success with just adding water to a pan with burnt-on stuff and heating it to a boil. Scrape with a wooden spoon, see if it comes off. If it’s only barely starting to come off, heat for longer, try again.
Coca-cola, even if flat. Gets a gleam to even the most burnt of pans, if left overnight.
Gross, eh?
Note - Do not use your thumb nail to get off that last little gunk in the corner of the pan.
I had a gnarly 13x9 pan from making chicken wings for New Year’s Eve. After repeated soakings, I finally made some headway last night, and managed to get it clean by scrubbing and using my thumb in the corners.
I now have BBQ chicken scrunge embedded under my nail, and it hurts. Can I get an infection?
Probably - I’ll be scraping it out today at work with a paper clip. 
This always works.
If the paper clip gets stuck under your nail, you can use your lawn mower blade to get it out. If the mower blade gets stuck, you’ll have to use something even bigger and inappopriate-er to scrape it out. Perhaps a trident missile. 
Buy Teflon saucepans. :o
What kind of pan?
Non-stick pans should not be an issue unless you’ve ruined the non-stick coating, in which case, you may want to consider replacing the pan.
Pretty much everything else should respond to Brillo pads or Barkeeper’s Friend scouring powder.
For truly wicked messes on the outside of pans, there are “industrial” products such as Sokoff (Soak-Off) and Carbon Cleaner available at restaurant supply shops.
I came in here to recommend this.
The basis of the Fabric softner sheet thing, I would think, would be the oil/petroleum in the sheet that would help unstick the gunk. Why not try plain cooking oil?
I’m bringing up an old thread but this is some good info that has always worked for me.
When I have a pan I want to clean, I pour some salt in it (not sure how much but enough to cover the majority of the pan), then I heat up the pan on the highest setting until everything gets nice and hot. Then I wipe the salt off with a wet paper towel. The salt acts like a really fine sand paper but I haven’t had any issues with it scratching the pans.
It always surprises me that I’m always the first person to mention the most obvious solution. There’s an everyday product, found in most kitchens, that is specifically formulated to removed burnt on food from cooking surfaces.
It’s called oven cleaner. That’s what it’s for.