Do I need to pay US state taxes as a UK resident?

I'd suggest reading the Illinois Department of Revenue website since all of this information is clear and up to date there, as against paraphrasing it here!

Does anyone know about Illinois?

Illinois is a residency state.  Once you move your residence out, you no longer need to file.  If you are maintaining a residence then you need to file, though Illinois state tax is based off of Federal Taxes, so you will be able to exclude upto $80,000 of foreign earned income as long as you are out of the country for a period of 12 months.

I know this is an old thread, but since its been previously discussed, I thought I would add here... I still own a home in Colorado.  I will, of course, file this year since I worked there in 2009, but am I correct to assume that I will need to file every year as long as I own a home?

Income Tax - Living Abroad

Does a Colorado resident who moves out of the country have to continue filing a Colorado income tax return?

A Colorado resident reporting U.S. federal taxable income must continue to file Colorado returns as a full-year resident no matter how long he or she is out of the country. Most such individuals are working on a temporary assignment, and return to Colorado. Because of this, there is a presumption that people from Colorado working in foreign countries are still Colorado residents.

All foreign income that is exempt for federal purposes is also exempt for Colorado purposes.

Individuals who abandon their Colorado domicile and become permanent residents of a foreign country no longer have to file Colorado returns. However, they would have to file a Colorado tax return as a nonresident if they had Colorado-source income (e.g., rental income). Such individuals bear the burden of proving their abandonment of Colorado residency. Continued Colorado residency will be presumed if the individual has not severed all Colorado connections; for example, if the individual still carries a Colorado driver’s license, votes in Colorado by absentee ballot, and/or still owns a home in Colorado, or returns to Colorado.

Source: http://www.colorado.gov/cs/Satellite/Revenue/REVX/1200408332136 [nofollow]