Just wanted to add a note: Most people who aren't making anything won't be posting, so results will be drastically skewed. So for anyone here getting discourage because they think their a minority - think otherwise (And then get back to work on trying to get your own setup ;))
People on H1B, like me, simply can't. It is ilegal to have any income coming anywhere else other than the employer associated to the H1B... It is ilegal to even make money on ads on a blog... this completely sucks and is very frustrating.
Without going into much detail, permanent establishment generally defines when a business is treated as operating in a country. The specific conditions are set forth in various tax treaties between the US and other countries. Generally, having an employee residing in the US and working for the business (whether or not as owner) is usually treated as resulting in a US permanent establishment, meaning the business is treated as operating in the US. If you are from a country which does not have a tax treaty with the US, the issue is generally much simpler: does the business have any income-generating operations in the US?
The second consideration is sourcing of income. IRC 861 and 862 define what income is US-sourced and what income is foreign-sourced. Generally, income from US customers or US payors is US-sourced income, and the same income from foreigners is foreign-sourced. For income taxation purposes, this distinction doesn't matter but it does matter for non-tax purposes. The H1B restricts the employee from engaging in US employment or business activities, but does not restrict their non-US employment or business activities.
A blog hosted on a foreign host, targeting a foreign audience, and earning foreign ad dollars is not a US business and generally should not violate the H1B rules, however you need to talk to an immigration attorney to make sure the analysis applies to the specific blogging activities you would be engaging it.