The easiest move is to buy a new Teflon pan–this one is very old, and I’ve been meaning to replace it for a while. But I’ll invariably burn some crud on the new one, so I’d like to solicit opinions on anything beyond “Just keep throwing them out.”
Old teflon pans should be thrown out. The chemical in old teflon coating is
perfluorooctanoic acid — or [PFOA]. PFOA can stay in your body for a long time. Cookware manufacturers eliminated PFOA from production of non-stick cookwear several years ago.
What he said. Pitch it, buy a new one and treat it well. Mostly, avoid high heat for sustained lengths of time.
Toss it. Please. There’s no reason to keep it around anymore.
Soak is the only way I know. If you scrub it you’ll eventually remove the coating then its about as worthless as the crudded up one.
I won’t repeat: throw it out. But you know, you need to…
I wouldn’t ordinarily use it on nonstick but, if yours is already wrecked, my coarse bronze wool makes short work of any cruddy clumps.
I’m sadly in agreement, if it’s already “very old” (although for some people that’s 2 years, and some it’s 10+) with burnt on crud, it’s best to get rid of it. Otherwise, if I have crusted crud on a non-stick pan, I generally try simmering a centimeter or so of water in the pan on medium heat with a splash of dishwasher soap in the water. After simmering for 5-10 minutes, take out and scrub with a stiff but non abrasive brush. If that doesn’t work, I suspect it’s well and truly done for.
Over the years I’ve learned that for any non-stick coated pan the best things to do is NEVER cook at anything higher than medium or say 60% of max heat. It kills pans. And to never believe the pan is dishwasher safe even if it swears it is. 
Consider a well-milled cast iron replacement. Unlike the pebbly-textured cast iron pans, they don’t require incredibly futzy upkeep of the cooking surface (although they do cook better if you leave an oil film on the surface in perpetuity), they are basically nonstick pans from the start. No weird complicated chemicals involved.
From today’s market I recommend Finex or Field.
I second the cast iron suggestion.
I third it.
Cast iron pans will last longer than any of us will. Even battered, rusty, baked-on-stuff-left-for-years cast iron can be soaked and scrubbed clean and then re-seasoned and it’ll be fine.
If you can’t use cast iron because you can’t use a heavy pan, I’d recommend a ceramic lining. Ditch the Teflon, even the newer versions may well have something unpleasant that you’ll eventually wind up eating.
Fortunately, you’re probably getting your nutritional requirements for PFAS from drinking water anyway.
Still, I’d dump the old pan and replace with cast iron or carbon steel, anyway. No coating to scratch off, can be heated to any temperature short of melting without damage, and you can scrape them down and re-season as necessary.
Stranger
How about granite for non-stick? I just bought my first one a few months ago and I love it.