Kavan Peterson:

Schools spend fewer dollars per student in Utah than in any other state, but more fourth-graders there improved reading and math scores over the past decade than in more than half of the states.
Maine, for example, spends nearly twice as much on a comparable student population — $9,300 a student vs. $4,800 in Utah. But fewer Maine fourth-graders improved their math scores — and their reading scores actually declined in the past decade.
Both states ranked just above the national average on 2005 national reading and math tests, known as the National Assessment of Education Progress, or NAEP. But Utah stands out for its success in boosting the number of students to pass the tests since 1992, the first year of state-by-state NAEP testing, despite ranking dead last for spending.
State by State Test Scores and Per Pupil Spending (.xls)

UPDATE: a reader emails:

The relevant comparison to make on the data on school funding and NAEP scores is Minnesota versus Wisconsin. We have a somewhat higher level of students eligible for free or reduced lunch, over 10% higher funding per pupil and lower NAEP scores.