If you need to send an anonymous letter - hopefully for good (say, whistle blowing) and not evil - you can still do so.
Use a fake return address (duh).
Drive to a mailbox far away from your work or home. Pick a mailbox that has no security cameras. Don't go into a Post Office, where there will be security cameras.
Turn off your phone before going anywhere near the drop location.
(This is all coming from a PBS documentary about how they went about the 2001 anthrax attack investigation.)
Buy the envelope, stamp, and any mailed material (eg paper) far from your home.
Exclusively handle all the materials to be sent in a clean environment far from your normal haunts. You may want to wear a hair net, breathing mask, and gloves. Do not lick the stamp or envelope.
Be careful about handwriting anything, if authorities may have any samples of your handwriting — as for example on prior letters addressed, or archived forms filed. Also, do not use a computer laser/inkjet printer, which may add unique invisible tracking codes.
After leaving behind your own phone, be sure not to use a vehicle with its own phone (OnStar etc) or any RFID transponders (eg tolltags, which can be read for traffic jam analysis even on non-toll motorways). Similarly, put aside any personal ID or payment cards (passports, some driver's licenses, mass-transit stored-value cards, etc) which may have remotely-readable RFID transponders.
Try to arrange for your phone, computer, or residence to continue giving off its usual signals of your presence – so that the period of the letter mailing doesn't show up as a suspiciously idle time for you.
Avoid all private and public surveillance cameras, or disguise yourself (and your car's license plate from automated readers).
Still:
Even with all these steps, it's likely the individual's capability to opt out, with effort, from being tracked will soon be obsolete. It will be too cheap and appealing to video-record all public spaces, or even regularly dust all public spaces with unique molecular tags so that when examining an artifact later (a letter, vehicle, article of clothing, etc), all other places it has recently been are evident to careful analysis.
Instead of just driving to some far away place and come back, I'd pick a mailbox that's close to something where you might go sometimes but that's not close to your house either.
For example, you could go to Ikea buy something there (with a credit card to leave a log of a transaction) and mail your letter. Ikea because they aren't that many Ikea stores but it's not out of the ordinary to drive quite a while to go to one.
My point is that if you have reasons to want to send an anonymous letter, you might want to make sure that a drive that doesn't fit your regular patterns can be explained by something reasonable.
edit: I'm not sure the credit card is a good idea. Likely not. It might be better to pay cash, and keep the receipt. This way, you can't be immediately cross-referenced, but if asked, you have an alibi. Yeah, I really don't know. :)
MI5 had a nickname of "Box" or "Box500" because postal mail was sent to "PO Box 500".
The letter would be put in an envelope. That envelope would be addressed with a department (but not a name). That envelope would then be put in another envelope. The outside envelope would be sent to Box 500.
It is kind of weird that in the 21st century we're re-learning ancient tradecraft from retired spies.
Use a fake return address (duh).
Drive to a mailbox far away from your work or home. Pick a mailbox that has no security cameras. Don't go into a Post Office, where there will be security cameras.
Turn off your phone before going anywhere near the drop location.
(This is all coming from a PBS documentary about how they went about the 2001 anthrax attack investigation.)