Guilt by Association

Disclaimer: Do not try this at home! In some countries, if you do, you may not have a home much longer. We are what you call experts - which makes us prone to dole out ridiculous unwanted, biased missives masquerading as some sort of insight. While, in reality, it is just meant to alleviate boredom. **

The disclaimer really admits our inability to come up with a comprehensive description of a framework which would achieve the goal of having fun and privacy on the internet without governments misunderstanding a desire for privacy or a sense of humor.

A brief look at philosophy and legal treatises on government explains why that is: nowhere in the mountains of documents on which modern states are based will you find the requirement that government must have a sense of humor.

Worse, other than the U.S. Declaration of Independence, we could not find even the simple concept of happiness enshrined in the founding documents of modern states.
Note: If you read the Wikipedia page behind the link, skip the table section "Indictment".

Given the way the world works these days, attracting the attention of your own government often means other governments get to share this, with utterly unpredictable consequences.
We limit our enumeration of items of fatal attraction to ten items, any more could trigger depression in our more sensitive readers.

1) Take flying lessons.
This is 100% guaranteed to work. 

2) Have interesting friends.
Note: Stay away from religious friends, unless you are friends with the pope himself.
"Friends" is a loose term, "contacts" is used in many official documents, but even that is not sufficient. You may never have any contact with a person or organization, it may be enough that they have your email address or your postal address, which they may find on the web or which someone of ill will gives to them. It is called "hops", and it is not friends of friends of friends as the media tries to explain it to us dummies. Because if it were "friends", the blogster would be friends with assorted presidents, princes and some very gross folks.

3) Use strong encryption.

4) Set up a TOR relay.

5) Set up a TOR hidden service.
A "Hello World" page is enough. Just for a couple of weeks or months, no need to publish the address.

6) Try steganography.
Note: The lazy version to avoid the individual items 3 to 6 is to simply visit the TOR website. Depending on your country of residence (as defined by the IP address of your machine), the lazy version may work just fine.

7) Do not use a credit card (provided you live in a country where almost everybody else uses cards) .

8) Have a Twitter account.

9) Have a Facebook account.

10) Publish anything (the quality is irrelevant) about any or all of the above.

On second thought: It may be enough to own a cell phone and make a call near an "interceptor" tower. In the U.S., 19 such towers have been found recently, according to this Venture Beat article. In some countries, using a burner phone is sufficient to attract attention. 
Technology is advancing fast, so the list is getting longer as we write this, and algorithms are getting more complex, allowing individual actions each considered innocuous to be combined into something a computer considers worthwhile to check out (in legal terms "odd").

We have heard rumors about one joker who puts a bogus message at the end of emails, something like:

-----BEGIN PGP MESSAGE-----

Version: GNU PGP 2.0.1
qAlQR1DBwk4DepqGz+tv7awQC/sGOyvgkqLDEz3QOc4AkDuoTVl9O4y7X460lR47
w77OngPn3z/01yEpVDmkfrpdXKYmVhylICPg1yvlYTyx6EW5LIOYt1yuxLc+bjKS
piwrBdCxz5+VT8z9IQz7Blu75GBP5YMJyhZUgwFRDahPITz0ziqL9nBZeUX47PGL

-----END PGP MESSAGE-----

Apparently, he does this when he emails environmental organizations or liberal politicians.
To us, this is twisted because it exploits the fact that emails get scooped up as they travel over the wire/the cable/through the air.
So, even if the recipients block the guy, some computer through which the email is routed may think there is something nefarious going on.

Disclaimer repeat: Do not try this at home! In some countries, if you do, you may not have a home much longer. We are what you call experts - which makes us prone to dole out ridiculous unwanted, biased missives masquerading as some sort of insight. While, in reality, it is just meant to alleviate boredom.

** There are many countries where you do not have to do anything. Just talk on the phone, send an SMS, an email. But if we list those the media have already listed for us, where's the fun?

[Fake update] Did we test any of the listed items? Yes, some of them, not on purpose but they work.