Down the drain? Does it depend on the type? With bacon fat, I usually let it solidify in a cup lined with foil, and then throw it out. With used canola oil, I'm not quite sure what to do because it doesn't solidify.
Never down the drain. We've had a few incidents in my neighborhood where the sewer pipes were clogged with fat, and a few people's basements flooded with sewage as a result.
For fats that solidify, let them do so, then pitch them in your regular garbage. Chill grease in the fridge if you need to get it to harden up. For ones that don't solidify, pour them into a sealable (hopefully non-recyclable) bottle, and throw the whole container away with your regular garbage.
It's possible that your area might accept cooking fats & oils as part of a recycling effort. Ours does for motor oil (I live in Maryland).
For restaurants, some places (eg, the state of Maryland) require a system for catching grease that's been washed down the sink. It's my understanding that they're fairly expensive (a couple thousand dollars US), but the fines for not having one installed may be even more, and they won't let new restaurants open without one.
Composting used oil can be done. Since it is organic it makes great earthworm food. But as Joe mentions: be careful to make sure you're doing it right. Large quantities of oil used to cook meat can attract vermin to your compost, and lots of oil in your compost can form hydrophobic barriers, reducing water & airflow.
Perhaps a safer option: After allowing used oil to cool you should put it in a small sealed container and throw it out with the trash. You can save empty jars for this purpose. If you produce large amounts of oil you may need to take it directly to your landfill, oil recycling station, or ask a local restaurant if you can drop off your oil there.
I advise against pouring it down the drain. It will clog overtime.
Also, you can reuse most oil several times. Deep-frying oil can be filtered and reused 3-4 times (more depending on the quality and your comfort). Bacon fat can also be filtered and then stored in your refrigerator.
Unless you fry very often, you can store the twice/thrice/whatever used oil and use to saute or as an ingredient in cakes and breads that call for oil. You need to keep track a bit, since you don't want to put the oil used to fry shrimp into cookies, but it might work well to saute onions for shrimp tiki masala.
Bacon grease can likewise be reused. Its my personal favorite for frying onions used in heavy curries from northern India and hearty meat dishes like stews. Simply dump into an old can or a pyrex container, cover in cling film or foil, and store in the fridge for a week or two (it can pick up odors, so not too long), or freeze in cubes for future cooking (would probably keep a year or so).
Other fats can be put to good use: chicken fat is used as a condiment in Central European Jewish food, for instance.
If you do fry a lot, you can save the used oil and make biodiesel. The process if fairly simple if you have a few days to let the product sit.
When I have some spare in a pan after a bit of a fry up or whatever I get the end pieces of bread from the current loaf and pour the fat all over them, then I let it soak in and then dry up for a bit and I put that out for the birds.. They love it - There's a wood pigeon here that loves bread with bacon fat!
Bacon grease can be a real pain in the ass. Pour it while it's liquid and hot into an empty plastic bottle and you risk burning yourself or burning a hole in the container. Wait for the grease to dry in the pan and you've got a hell of a clean up job on your hands. No matter what, leaving bacon grease to sit in your home will cause a stink. Not sure about you, but I don't like to think about or smell bacon very long after I've eaten it. So what to do?
Unfortunately, there doesn't seem to be a silver bullet out there. Many recommend pouring grease into a non-warpable container like a Chinese takeout box or a milk carton, but not everyone has something like that laying around.
An option I've found useful: line a glass or mug with aluminum foil and pour hot grease in there. To speed up solidification, put the ensemble in your freezer for a few minutes, then pull it out, and trash the grease-foil -- preferably in a bin outside.
Some utilities have or are starting residential cooking oil recycling programs. They will either have a drum to pour oil into, or a cabinet to drop off a bottle. If there is no program in your area, the trash can is the best option.
You should never dump oil down the drain, as it can cause odours and back-ups in your home and the sanitary sewer collection system.
You can learn about the program in Hillsborough County, Florida by visiting: www.hillsboroughcounty.org/core
Many restaurants have collection containers in back and will accept your fats while those using biodiesel may pull their vehicle up and fill up for free!
It depends on the area, but I have heard of people going across the country on restaurant freebies! Check it out some more, to see if this is viable in your area.
I don't deep-fry so I never have multiple quarts of used oils. For a skillet full of used oil with too much crumb in it to reuse, I use a lot of Dawn and very hot water to fully emulsify the fat and then wash it down the drain with hottest water. I'm on a septic tank in the country for nearly 20 years with no problems.
I save bacon fat that isn't overheated to fry tortillas and veggies headed for a stew or stir-fry. I keep bacon-fat in the fridge, although many southern cooks just keep it in a pot by their stove.
There are now (2018) plenty people using old chip oil for bio-fuel in their old diesel cars. Do a few web-searches for "waste vegetable oil recycling" "wvo recycling" "used chip oil collection" etc. and you might find someone local to your neighborhood who will arrange to collect it for free. I do this in Grimsby U.K. along with many others.
In my area (Vancouver, Wa), the recyclers will take used engine oil, but NOT used cooking oils! If I'm desperately trying to do the perfectly right thing, a couple of the local restaurants will let me dispose of my oil in their collection containers, but that's a pain in the A** So for the past 20+ years, I've simply mixed a couple of tbsp of dish detergent (that's enough for 1/2 gal of oil) into the oil and then slowly drizzled it down the drain w/plenty of Hot water. There has Never been an incident with the sewers in my neighborhood!