I enjoy these sorts of things considerably, so I thought I'd pass along the ones I know. They are historical journals that are being re-journalized as blogs.
The Diary of Samuel Pepys
There is absolutely no better way to get the dish on the seventeenth century; this contribution by Phil Gyford and others is the most elaborate of the historical journal blogs, and is interesting in that it is marshalling the power of the blogosphere to develop an online scholarly apparatus for the diary. This reminds me a bit of the recent discussion, started by Jason Kuznicki, about the possibility of a history wiki; the structure of this diary is rather different in some ways from wiki, but it has many interesting similarities to the sort of thing he seems to have intended. It also reminds me a bit of questions about whether blogging can be a mode of scholarship in a fairly narrow sense; if the blogging is along these lines, I think there's a good argument for it. One of the interesting new features is the topic map, which is way cool.
David Brainerd's Blog
Rebecca gives us a look at the missionary work of David Brainerd.
John Wesley's Journal
Seymour guides us through Wesley's journal.
(I especially like Wesley's comments on Law for October 23: "Philosophical, speculative, precarious; Behemish, void, and vain!" I've written briefly about Law's interest in Boehme elsewhere.)
All three of these are early modern. Does anyone know of any others?
(Cross-posted to Houyhnhnm Land.)
UPDATE: Sharon and Caleb provided additions in the comments. Apparently the blog "Keywords" some time ago had a post on books that are being blogged, which includes several journals, including Da Vinci's (hat-tip to Kmlawson at Muninn).