Does your pot frequently runneth over? Are your stove burners caked with spots from former tenants? Do you set off the smoke alarm before you even begin to cook? It might be time to give those stove burners a good cleaning. Here's how.

1. Remove them.
Wait for the burners to completely cool (we can't stress this enough!), then remove them from the stove top. Most should slide out with a gentle tug and lift from the connection point, but if you have questions, refer to your manual (or find your stove's manual on Manuals Online).
2. Rinse them with soap and water
Using a cloth and a bit of mild dish soap and water, rinse any residue from the burner coils. Take care not to get any part of the the electrical connection wet, and don't submerge any part of the burners.
3. Use baking soda paste for tough spots.
If there's any cooked-on food residue that won't come off with the soap-and-water mixture, use this method: Make a paste from baking soda and water, then apply it to the tough spot. Give it about 20 minutes to sit, then scrub and rinse the burner.
4. Let them dry thoroughly.
Make sure the burners are completely dry before you try to replace them.
(Images: Flickr user SullyT64 Photography under license from Creative Commons, Flickr user dawnie cakes under license from Creative Commons)

Shaw's Original Fir...
My mum, who is fastidious on the cleanliness of her kitchen, always lines the drip pans (under the burner part) with tin foil. That way, when the inevitable boil over occurs, you just pull of the tin foil and reline it. No scrubbing necessary... and you don't need to replace the drip pans... ever!
I really hope this works. I have scrubbed and soaked and scrubbed, and I'm about to give up and just buy new drip pans.
I just put them in the dishwasher. Maybe I'm taking big chances, but they seem to be fine.
Drip pans are cheap and easily replaced when they're too dirty to clean. The COILS are what this post is referring to. They are not so cheap to replace, but they *can* be cleaned.
VJ,
You put the coils in the dishwasher? How long do you let them dry afterward?
This post is talking about the actual burners themselves, NOT the drip pans. You should NEVER soak the burners or put them in the dishwasher. That is an accident waiting to happen.
I'm sure you can use some of these same techniques for the drip pans. However, at $10 for a whole new set, I'd just buy the new ones.
I buy black drip pans to cover some of my "sins".. aka I can wait longer to clean them.. but the coils I've never attempted to clean properly. I will have to try this one soon!
You could get the coil wet. Just make sure they are completely dried before using it again, or you'd blow the fuse.
I recommend using foil guard under the coils, over the drip bowl. They're are like 8 sheets for $1.
Can't say I've ever had issues with the coils themselves *knock on wood*. When I was a cashier, people would bring in coils that were completely melted! It's amazing!
tin foil sounds better than buying the premade foil inserts at the store. Why didn't I just do that? sigh.
i'm sorry i dont understand why you would need to clean the coils... the drip pan of course by the coils? really? most of my drippings just burn off at the next use. seems silly.
Ah, Oneformybaby, but burning drippings off the coils stains the bottoms of your cookware.
Icky awful greasy stains smoking eugh.
Which is why I won't buy nice cookware until I'm somewhere with a gas stove.
Why the heck would you clean the COILS? They get RED HOT every once in a while, I think that would take care of most of it!!!!
@ Shelley - I let them dry a couple hours. It's moisture controlled in the apartment, so they're very dry by the time they're re-inserted.
@ Johnc - if you don't want whatever is spilled on them to reek when they get red hot, you want to clean them. If you avoid getting any grease on them (covers?) then you can skip cleaning coils.
I want my burner coils to look brand new. Has anyone used Stove Black? Is there anything else that will make them look new again?