No you can’t. Widgets are usually site-wide though there are a few themes that have exceptions. See > http://wpbtips.wordpress.com/2011/02/26/sidebars-and-other-widget-areas/ CSS editing may be possible if each page type has its own CSS class. However, I don’t help with CSS editing so I can’t say whether or not that is the case with Twenty Ten. I’ll flag this thread so it’s moved to the CSS Forum where you can get a definitive answer.
For regular static pages you have created (about, services, etc.), simply open those in the page editor and from the “template” pulldown in the attributes module, select “full-width/no sidebar” and update the page.
The sidebar will then only appear on post related pages (blog, categories, tags and archives pages).