Where can I download historical data from OpenStreetMap? I am interested in downloading an OSM
.pbf file of a particular city in previous years (say, from 2008 and 2010).
Historical OSM data is available in the OpenStreetMap Full History Dump file. You can dowload it as *.pbf or *.xml data. Extracs of selected countries can be downloaded from http://osm.personalwerk.de/full-history-extracts/ or from http://odbl.poole.ch/extracts/. I recommend you the OSM-history-splitter to generate extracts out of *.osh files and the OSM-history-renderer to render data from specific historical timestamps.
Another option is geofabrik website, which makes available OSM data in three different formats:
.XML for all countries and continents. The oldest datasets they have are from 2014-01-01.