Twitter: http://urls.api.twitter.com/1/urls/count.json?url=http://new... LinkedIn: http://www.linkedin.com/cws/share-count?url=http://news.ycom... These APIs are marked private (as opposed to Facebook's) so use at your own risk.
I packaged a few of the private ones with this weekend project: http://sharedcount.com Unfortunately, only Facebook does URL normalization for you, so dumb things like trailing slashes have a big effect on the count.
Is that true?
http://urls.api.twitter.com/1/urls/count.json?url=http://new...
http://urls.api.twitter.com/1/urls/count.json?url=http://new...
http://urls.api.twitter.com/1/urls/count.json?url=http://new...