I answered my own question partway through writing it with a visit to http://iqdb.com. Rather than delete the question, I made it a shill for iqdb (brought to my attention by Logan M. in this question's answer.) iqdb led me to this page that lists all the series and characters in this picture.
The far left pair is Lelouch and Nunnally Lamperouge from Code Geass.
Next to Lelouch and Nunnally are Izaya Orihara and his younger twin sisters Mairu and Kururi, from Durarara!!.
Next are Hiromi Souma and Aoi Yamada from Working!!. They're not actually siblings, but Aoi tries to make Hiromi into her big brother.
Then we have the Araragi siblings from the Monogatari series. (The reason I found this picture.)
Next to them are Shouma and Himari Takakura from Mawaru Penguindrum.
The pair on the far right is twin brothers Yuuta and Yuuki Asaba from Kimi to Boku.