I feel this is indeed a difficult question, as there are so many different approaches to define the best. Doug leaves it up to the individual bloggers, so I want to give fhree answers.
1. Most viewed:
Die völlige Zerstörung von Apameia am Orontes (30.4.2013, 4243 views)
For the top 15 in 2013 see Archaeologik 2013
Most recognized at google+ :
Most reactions had a blogpost related to treasure hunting: Faltblatt Raubgräber (24.7.2011) with 53 comments within a discussion on treasure hunting - indeed a discussion I finally had to stop.
There are several blogposts, which brought very interesting comments, helping in my own research. For example http://archaeologik.blogspot.de/2012/04/vergessene-siedlungen-groflachige.html#more was commented with a short link by Klaus Graf giving reference to written sources, which previously have not be correlated with the archaeological record in question - a small, but valuable contribution for ongoing work.
Invitation for print publication
compare Habitus - vom Blog zur 'echten' Publikation. Archaeologik (5.12.2013)
There are many reactions in real life, which I can not link to a single blogpost for sure. I came in touch with several colleagues in the UK and Scandinavia, resulting in a common proposal for an ESF research project regarding 14th century cultural changes. Finally the application was not granted, but nevertheless we had an interesting exchange of ideas. Probably Yersinia pestis - the missing ecological and historical dimension was at the heart of these contacts.
Doug also asked for the blogpost most proud of. 'Proud' is maybe not the right term, and I do not want to refer to single blogposts. I rather estimate the broad variety of topics valuable, trying to connect the past with the present and to put archaeology into the context of modern society. Maybe I should especially mention the series of posts on Syrian civil war, starting in May 2012 and collecting the most important information on the destruction of cultural heritage in Syria: http://archaeologik.blogspot.de/search/label/Syrien%20-%20B%C3%BCrgerkrieg .
- Bodenerosion 1342 - ein Rechtsstreit in Esslingen
- Unwetterschäden im Raum Tübingen im Juli 1342(?)
- Wüstungen im Blaubeurer Lagerbuch von 1457
- Heidenheim-Schnaitheim: Fragen frühmittelalterlicher Besitzstrukturen
- Doug's Archaeology (5.11.2013): Blogging Archaeology - http://dougsarchaeology.wordpress.com/2013/11/05/blogging-archaeology/