If you live abroad and have income, you will still have to file a tax return. You must also either have taxes withheld from your paycheck or pay quarterly estimated taxes if you are working abroad.
However, the tax bite may be substantially reduced if you qualify for a foreign earned income exclusion and the foreign housing exclusion and deduction. See IRS Publication 54, Tax Guide for U.S. Citizens and Resident Aliens Abroad for current amounts. You can download this from the IRS website.
But renouncing your U.S. citizenship to beat the IRS won't work, at least at first. You remain subject to U.S. tax laws for ten years after renunciation!
There is one bit of good news. While you are subject to U.S. tax laws, it is very difficult for the IRS to grab wages or assets located outside of the United States. Some countries, mostly in Europe, have treaties with the U.S. in which their tax agencies can cooperate with the IRS to collect from U.S. citizens, but most governments place a very low priority on working these kinds of cases.
You may also owe taxes to the government of the country where you reside. Some countries give you credit for taxes you pay to Uncle Sam; others won't. Also, estate and inheritance tax laws vary widely across the globe.
For secrets, tips and insider information on how to deal with the IRS, see Stand Up to the IRS, by Frederick Daily (Nolo).