I admit, I'm not an expert on the topic, but the Zooniverse project has two crowd sourcing projects : Old Weather is extracting information out of British ship logs, while Ancient Lives is transcrbing Greek papyrus scraps.
I also remember seeing a poster talking about reading historical scientist's journals, but I can't find it. I think it was recently; I thought it was ASIS&T 2011, but it might've been IA Summit 2012 (which doesn't have a list of posters that I can find). I want to say it was exploration logs (similar in vein to Louis & Clark), but I can't remember if they were just classifying what was in it vs. actively trying to transcribe the writing. It might have been the Junius Henderson notebooks, but to my knowledge, that was annotating the transcription and not working from images of the originals.
In trying to find that poster and/or project, I came across a list by Ben Brumfield of crowd sourcing transcription projects in early 2011, and his blog seems to be a great resource on the topic in general, but of note is that list is not all were successful:
According to the New York Times article, there was an attempt to crowdsource the Papers of Abraham Lincoln. The article quotes project director Daniel Stowell explaining that nonacademic transcribers "produced so many errors and gaps in the papers that 'we were spending more time and money correcting them as creating them from scratch.'" The prototype transcription tool (created by NCSA at UIUC) has been abandoned.
... I would assume that it would be possible to use the crowd source efforts to train an automated parser (train it on one page, then have it read the rest of the handwriting from that person), so that you can get the most productive use out of the volunteers ... but I don't know if anyone's doing it. (or if it works as well in practice as in theory; I remember seeing an example from a war journal where the handwriting abrubtly changes due to an injury)