Which countries allow pilots to fly over the age of 65 for International Part 135 Operations?
Australia, Austria, Brazil, Canada, Costa Rica, New Zealand, Russian Federation, Senegal, and Ukraine

According to a 2006 ICAO report (mentioned also in this presentation) (emphasis mine),


  Nine States (Australia, Austria, Brazil, Canada, Costa Rica, New Zealand, Russian Federation, Senegal, and Ukraine) have no upper age limit, whereas fifty-five have an upper age limit higher than 60 years, ranging from 62 to 72 years.


This, of course, applies only to domestic flights, not international flights, as I imagine you have already read about:


  The ICAO Council adopted on 10 March 2006 an amendment to Annex 1 — Personnel Licensing that increases by five years the upper age limit for commercial pilots operating two-pilot aircraft, subject to conditions. The new provisions become applicable on 23 November 2006 and read as follows:
  
  2.1.10.1 A Contracting State, having issued pilot licences, shall not permit the holders thereof to act as pilot-in-command of an aircraft engaged in international commercial air transport operations if the licence holders have attained their 60th birthday or, in the case of operations with more than one pilot where the other pilot is younger than 60 years of age, their 65th birthday.
  
  2.1.10.2 Recommendation.— A Contracting State, having issued pilot licences, should not permit the holders thereof to act as co-pilot of an aircraft engaged in international commercial air transport operations if the licence holders have attained their 65th birthday.


Note that the ICAO typically gives constituents recommendations, not necessarily enforceable laws. Those are generally up to the countries themselves, which is why these nine are able to not have upper age limits.

I wanted some confirmation on the original list from something more recent, so I checked out a few sources. I was only able to find information for two.

Australia

From the Civil Aviation Safety Authority, it is noted that the ICAO age limits for pilot in command (PIC) and co-pilot are not relevant in Australian domestic flights, and seems to imply that age does not affect the ability to hold a pilot's license.

Canada

The best I could find was this article from The Globe and Mail, originally from 2009 but possibly updated in 2012.


  There is no upper age limit to acquire or renew a pilot licence in Canada - all you have to do is log the hours, complete the training and pass the medical exams, when necessary.