The think tank, Iraq Analysis, based in the UK, maintains a list of public opinion polls that have been conducted in Iraq with results published in English. Many are by professional polling organizations such as Zogby and Brookings (for example see the Brookings Iraq Index).

The URL of the list
http://www.iraqanalysis.org/info/55

In addition, see the results of yesterday's release of BBC/ABC news poll conducted in Iraq -- there is a downloadable .pdf of summary results.