I have a short-stay, multiple-entry Schengen visa that expires in 2016. I entered Europe on the 23rd December 2014 and stayed there until the 15th January 2015 (24 days).
Now I want to go to Europe from 22nd May 2015 till 29th August 2015.
Is it possible with my existing visa or do I need a long-term one?
You can reenter and stay for up to 90 days. On May 22, the end your first stay will be more than 90 days in the past and therefore would not count anymore.
But May 22 to August 29 is 100 days and you can't stay that long on a Schengen short-stay visa. You need to either shorten your trip, spend some time in a non-Schengen country during that period or secure another type of visa/residence permit.
See How does the Schengen 90/180 rule work? for some explanations on the maximum stay rules and a link to a calculator.
