Angus King, the ex-governor of the state of Maine who was instrumental in the mass roll out of the one-to-one laptop initiative in the state's middle schools characterises the benefits of the programme as follows:
to significantly improve writing scores
to improve behaviour and attendance
provide true 21st Century skill
and all for the same cost as the state snow-ploughing budget! http://goo.gl/FMRr9
It's interesting that even this (at the time) highly innovative project

had standardised testing in mind as an achieveable outcome, which, given the US obsession with test scores as a means of identifying teacher performance (see Race to the Top; http://goo.gl/yOltm ) is hardly surprising.
Of more surprise is that this objective was actually achieved.
"Analysis of these average scale scores indicated that, in fact, there was a statistically
significant improvement in writing scores after implementation of the laptop
program" (Silvermail 2007)
Although writing is only a part of the range of testing it was an area for improvement as noted by Angus King.
However, outside of Maine there has been a more lukewarm response to one-to-one initiatives, as highlighted by the New York Times; http://www.nytimes.com/2007/05/04/education/04laptop.html?pagewanted=all
The articles states that laptops have been ditched as they have "showed little, if any, measurable effect on grades and test scores at a time of increased pressure to meet state standards." Note again the stressing of the importance of standardized assessment scores.
But as Scott McLeod points out on his blog, the types of higher order, authentic, 21st Century Learning experiences that an innovative laptop programme should be looking to achieve are unlikely to create an atmosphere conducive to higher standardized test scores: http://goo.gl/N0l1S
He also highlights key factors in lack of training and support to help these initiatives achieve their true potential.
Silvermail, D.L., Gritter, A.K. (2007). Maine’s Middle School Laptop Program: Creating Better
Writers. Maine Education Policy Research, University of Southern Maine.