This is a fundamentally important questions because it greatly impacts the defences you apply.
The measures you take to hide your identity from, say, a significant other or general member of the community may not be sufficient to hide from government oversight.
Many of the data breaches I come across have numerous Mailinator addresses in them for precisely this reason.
The easiest personal identifier that will match you to a site is your email address.
I'd also like to encourage those who do give online anonymity a lot of thought to leave their suggestions in the comments section, keeping in mind the target audience being your normal, everyday people.
Let's start somewhere extremely practical yet often not acknowledged in discussions on privacy and anonymity.
Of course the latter will usually also protect you from the former, but it also often comes with an additional burden to implement.
I'm going to focus on what's readily accessible to the bulk of the population.