For a home wireless router, you're trying to defend against hackers without physical access to your home from stealing your resources or snooping your network. Writing the password for your router down is almost by definition not a problem, since anyone physically in your home could already plug into your wired network.
For most other home applications, unless you believe the government or those with grudges against your are willing to go to a lot of trouble to hack you, you're probably still only worried about random or semi-random online attacks. Again, written passwords shouldn't be a problem.
If you're trying to hide your porn collection from your SO, the written password is probably not such a good idea -- depending on how computer-savvy your SO is.
Your online bank or PayPal password is another consideration -- if you have a piece of paper clearly marked "PayPal userid and password" sitting on your desk and a thief breaks into your house, well, why wouldn't he take that and try to drain your bank account too?
And so on. The point is, you can't ask the question "how secure is this" in a vacuum -- you have to understand what the potential threats to the resource being protected are, and which measures you are taking to counter which threats.
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For a home wireless router, you're trying to defend against hackers without physical access to your home from stealing your resources or snooping your network. Writing the password for your router down is almost by definition not a problem, since anyone physically in your home could already plug into your wired network.
For most other home applications, unless you believe the government or those with grudges against your are willing to go to a lot of trouble to hack you, you're probably still only worried about random or semi-random online attacks. Again, written passwords shouldn't be a problem.
If you're trying to hide your porn collection from your SO, the written password is probably not such a good idea -- depending on how computer-savvy your SO is.
Your online bank or PayPal password is another consideration -- if you have a piece of paper clearly marked "PayPal userid and password" sitting on your desk and a thief breaks into your house, well, why wouldn't he take that and try to drain your bank account too?
And so on. The point is, you can't ask the question "how secure is this" in a vacuum -- you have to understand what the potential threats to the resource being protected are, and which measures you are taking to counter which threats.