All right Mr. Pedant, yes, if you qualified to not have to file in the US, then you're probably OK not to file as a non-resident. However, if you're an adult non-resident with any significant source of income, you do have to file, even if that income is below the non-resident exemption (approx $90,000 USD) where you won't owe any income tax. But do note that the US is virtually alone in taxing non-resident citizens.
If you don't make substantially more than $90,000 and only have an income from a job (i.e., not self-employed, own a business, or have substantial investment income), it's not a huge deal beyond having to file a second tax return. Otherwise, it can mean major tax headaches. A friend of mine up here who's also a non-resident US citizen folded his one-man business and took a regular job because the tax benefits to owning an incorporated business in Canada were nullified after the IRS claimed their share (and then some).
The point being, yes, there can be serious tax consequences to having US citizenship if you don't earn your living in the US. I don't foresee renouncing my US citizenship anytime soon, but for a foreign national considering whether to pursue US citizenship, I would advise them to think twice about doing so without a compelling reason.