My drip pans are in some serious trouble, and soaking them overnight in soapy water only somewhat worked. I did some research to find better solutions, and as promised, I'm sharing what I found. Hopefully, no matter what type of stove you have, this will help you rid any stains of the unknown (Really, after a few cookings, one stain from another is indistinguishable, you know? It's black crust and all I know now is that it won't come off!)

First off, remember that upkeep is the ultimate best way to keep it clean. Clean it as often as you can (without wearing yourself out). The strategies listed first are cost effective, but if you would rather, or if it still is not coming off, try using the other cleaners suggested below. Most of the ideas come from tipnut.com BE SURE TO TEST ALL PRODUCTS ON A SMALL AREA FIRST. I don't want anyone ruining their stovetop on my account.

1 Way:
(for a porcelain enamel surface)
Clean and scrub with soapy water (don't worry, there's more!). Place paper towels soaked with ammonia over the "unknowns" as I'll call them. Cover paper towels with plastic wrap to keep moist. Let sit for a few hours. Wipe away. Be careful and watch the stove during this time.

2nd Way
(for surface, rings, and drip pans)
Do the same as above only with vinegar rather than ammonia.

3rd Way
(for drip pans)
Spray with ammonia and place in garbage bags. Close the bags to lock in the moisture, and let them sit overnight, or if it's a hot day, in the sun (allowing the heat to help). Scrub in hot, soapy water.

4th Way
(for drip pans and rings)
Boil water in a large pot, add 1 cup Cascade dish detergent. Stir and dissolve. Carefully use utensils to place drips and rings in water, then boil for 5-10 minutes

5th Way
(for drip pans and rings)
Mix tartar and vinegar together (1/2 tartar, 1/2 vinegar), and scrub over items. Let it sit, then scrub.

6th Way
(for drip pans and rings)
Boil, then take them out and place in hot, soapy water with 1 tsp. ammonia. Let sit 30 minutes, and scrub.

Cleaners/Materials to help:

•  Nylon or Rubber scraper (These are nice because they won't scratch the surface of the stovetop like metal would, but they still get the job done. A good substitute to wearing out your fingernails)

•  Magic Eraser Kitchen Scrubber--contains dawn. (It claims it can help with the stovetop, and frankly, I believe it. I have used other magic eraser products and let's just say it highly surpassed its expectations and saved more than a few walls from children's beautiful artwork. Magic is the best definition.)

•  Easy Off Stove Top Cleaner

•  Goo Gone Multi-Purpose cleaner (also works wonders. Gum? Stick from price tags? Anything gunky? =GONE)

•  Fantastik

•  409

•  Simple Green

If it still won't come off, remember to "try, try again", or use a different strategy or cleaner.

WORD TO THE WISE: Do not line your drip pans with foil. Although this is an easy clean-up, it is a fire-hazard. It can cause electric shock or burn and stick to the pan. On a gas stovetop there is risk of carbon monoxide poisoning, too. I definitely prefer to be safe than sorry, and I'd prefer a few scorch marks on a drip pan over more than a few scorch marks covering my entire house, or even worse, me.

References:
https://tipnut.com/8-cleaning-tips-for-crusty-stove-tops/
https://www.ehow.com/how_2203143.html
https://www.ehow.com/list_7637058_cleaning-tips-stove-top.html
https://www.mrclean.com/en_US/magic-eraser-kitchen-scrubber.do
https://www.marthastewart.com/344815/dirty-cleaning-job-solutions/@center/277000/homekeeping-solutions#334544
https://www.geappliances.com/search/fast/infobase/10000830.htm
Stovetop:
https://3.bp.blogspot.com/_ClSU4iSXUgU/S5msAyEk1AI/AAAAAAAACfo/LF55utObod8/s400/Stovetop.jpg
Mr. Clean:
https://cdn.alice.com/images/products/1282541/300.jpg?1329254587
Goo Gone:
https://www.homedepot.com/catalog/productImages/300/e1/e10e19f7-4646-4ff2-b5f8-e57417f29437_300.jpg
Nylon Scraper:
https://www.city-data.com/forum/attachments/house/41055d1241482903-removing-wallpaper-pampered-chef-nylon-scrapers.jpg