How to remove the 'gunk' from cooking that builds up on items around the stove?

Believe it or not I use gel hand sanitizer. I keep a pump bottle near the sink for not only hand use but surprisingly enough it will remove even the most stuck on labels and well...basically all tough grimy dirt.

I suggest an orange oil cleaner. I keep a spray bottle and use it on outside of pans, sink etc. It is a work horse cleaner used in cleaning lab glassware( used for wax and oil preparations) where I work.

Dawn dish soap, a non abrasive scrub sponge, a toothbrush and a little elbow grease and the tea pot is SPOTLESS! :)

Spray it with oven cleaner. let it sit for 5 minutes and wipe off with towel ten rinse off and shine it up !

Thanks folks! I'll put a few of these to the test & let you know what works best. FYI it's an OXO stainless steel tea kettle - not the prettiest thing in the world (dreams of enamelware), but will look a whole lot nicer without the greasy buildup.

Used coffee grounds! i sprinkle them on, scrub a bit, and the grease comes off.

Also, Greased Lightning...works great on anything thick and greasy...if you have problems getting either Dawn Power Dissolver or Greased Lightning, try Ace Hardware cleaning section.

Dawn Power Dissolver, you spray it on the dry surface, let it sit 15-30 minutes, wipe, rinse/wash. It works really well on stubborn or even burnt on grease. Good stuff.

I'm a firm believer in the magic of white vinegar. Ammonia is a close second. I haven't tried Dawn dish detergent, but have friends who swear by it. Another good grease remover is Simple Green; I've had success with that. Once you get the tea kettle cleaned off, I recommend a monthly run through the dishwasher - I have a stainless steel olive oil can that I keep close to the stovetop and it gets pretty sticky. A good hot dishwasher run once or twice a month keeps it from building up.

There's something called Japanese magic erasers and you can get it from most Japanese supermarkets. It's amazing, you don't need soap, just water. It cleans off most grease.

Here's what I've tried that seems to work:
1. You need a degreaser to cut through the fats/oil of that sticky greasy film on the tea kettle. I find that Dawn dish detergent really does live up to it's advertising. Soak in hot soapy (Dawn) water and scrub with a sponge or scrubber to see if it will come off. If it works, you're done. If not, go to #2.
2. Make a thick paste with baking soda and water. Coat the kettle and leave it a couple 2-4 hours or more if needed.
3. Scrub the dickens out of the kettle with a steel wool pad, like SOS pads, or a sponge with a scrubber side, like a Scotch Brite sponge. This part is not recommended for enameled kettles. If you have one of those, wipe the kettle down with a sponge or towel and rinse.

Ammonia. Unless it's aluminum. Same for the wall use the recommended dilution and open the windows and wear gloves---it really stinks.
Be aware NEVER mix ammonia with bleach as it creates a toxic gas.

I hate using the ammonia and have to leave the room when the SO does the walls the ceilings, but it's one of the cheaper sure fire ways to remove build ups of grease.