For cleaning keyboards and other computer components not reachable with a cloth, I generally use a can of compressed air.
However, the can is empty. What else can I use that would be a general household item?
Here are some methods for keyboard I use:
Generally for computers I often use a vacuum cleaner and reduce its power to the middle (it depends how powerful is your vacuum cleaner - adjust it for your needs )
I insert a large diameter drinking straw [Starbucks has them in their Computer Cleaning Section of every store);-)] into the slim angled attachment which comes with most vacuums, I then tape the straw to the outside of the attachment creating a seal. It is a simple matter then to take an ESP Brush as mentioned above and use it to brush the dust into the straw which sucks it into the vacuum cleaner. Where it goes from there I have no idea!
I have encountered a similar problem while cleaning dust and grime off PCBs for re-soldering/repair. Usually, the dust has accumulated over time, and due to moisture which can't be removed with compressed air.
Using a special ESP brush (size depends on each case), or a simple paint brush but ensuring correct ESP procedure clean surface and around/under gaps and components.
A small amount of Isopropanol (Isopropyl Alcohol) can remove persistent grime.
Harder cases may require a stiffer brush.
This is useful for cleaning motherboards, GPUs, fans and heatsinks. If cleaning a CPU/GPU die, take care and use some Iso., both on the die and the heatsink contact. Always reapply thermal paste after.
For keyboards, mice and other external peripherals, use cotton swabs with Iso. Keyboards (Desktop, mostly - laptops are difficult) can have their keys removed to clean between the key wells.
I was about to make a special tiny nozzle for my hair dryer (on cool of course), before I discovered a powered duster and bought that instead. You asked about a household item, so I'd go with the nozzle. I also briefly considered a balloon and a straw...
Instead of expensive cans of air, I use the blow gun on my cheap ($50-on-sale) 1-gallon compressor. There is a slight chance of water droplets forming, but it won't be as bad as human breath or the stuff that often falls into keyboards.
For larger-scale cleaning, I use my electric leaf blower. I take my desktop computer outdoors once a year, open up the case, and blast away! This works well on furnace filters, too.
Depending on how the crevice to clean is shaped, an old (but reasonably clean) toothbrush can work quite well. This seems to work well on the narrow spaces where plastic pieces come together, or decorative grooves in a device, where dirt or dust sometimes builds up.
How about just using a drinking straw and blowing out the dust? I had pretty good luck blowing dust out of a CPU heatsink that way. Or, maybe blow up a balloon and wrap the end on a straw for more force.
Breath is humid (relative humidity of human breath is 100%), so don't try this for anything that may be sensitive to moisture.
Note, prolonged blowing may cause dizziness.
Although I haven't tried it, I would imagine a bicycle pump would work. If you taped the "straw" from your old can to the end you could probably make it more directional and higher pressure. The adapter for pumping up footballs might also help in this regard.
I use sharp ended objects like toothpicks or mini screwdrivers. Weirdly, it's been a passion for me since childhood to clean such spots.
Anything that creates a stream of air:
I used to have a computer shop have blown out over 1000.
For a keyboard, I like the compressor with a nozzle as it is hard to blow them out and they are not very sensitive.
You can even vacuum on the keyboard.
The downside to the compressor is you can get some moisture. I have never lost one to moisture but for the motherboard, I prefer the shop vacuum.
Block the fans before blowing them out. I use a small screwdriver. With a compressor, you can get enough speed to spin (wreck) the bearings.
The power supply will be the dirtiest. Blow it out in each direction.
It is very hard to get into a laptop to clean it, but more important is it is smaller and the little fans and little fins can get impacted.
To add to existing answers: one desperate but great way of cleaning really messy keyboards is the dish washing machine. Place the keyboard key-face down and run the program, including detergent and all as you would your dishes. You can also wash some of the usual things with it as long as they are not too dirty (mugs, cups, plates as long as there is no food on them).
If it is a wireless keyboard make sure you remove the batteries first!
After the wash make sure you allow the keyboard to dry completely. Shake as much of the water out as you can, then place it close to an open window or onto a radiator. Don't use it, until you are confident all the water has evaporated. Water will not normally damage electronic equipment if there is no power.
But keep this as a last resort - in some cases the keyboard will after all not survive this operation. My own experience with this has seen no losses so far though. Anyway, this hack is very appropriate if you were considering to bin the keyboard rather than cleaning it.