I know that QGIS and unmet dependencies seem to be a common theme on this site, but this most recent one is a known issue. Through the standard Ubuntu updates in 14.04, at some point QGIS 2.8.1 has an unmet dependency with libgdal .so.1-1.11.1 and gets autoremoved. The solution on the ubuntu-gis list is to upgrade to the nightly 2.9.x version.
However this is not without its problems: Strange circles have appeared on QGIS map? The circles appear for me in 2.9.x and I can't get them to go away.
There is currently no accepted answer to that question, so I wonder if there is some other way to install this vital package.