Hydra are at least responsible for some of the events of Avengers Assemble.
Be warned that this answer is going to be dropping spoilers from multiple areas of the Marvel Cienematic Universe, including Avengers Assemble, Captain America: The Winter Soldier, Avengers: Age of Ultron and Agents of SHIELD.
In Agents of SHIELD S3E6 "Among Us Hide...", it has been revealed that one of the members of the World Security Council during Avengers Assemble (the one that ordered the nuclear strike on New York City) is a member of Hydra. Interestingly, this member of the World Security Council was not present during the meetings of the World Security Council in Captain America: The Winter Soldier.
Although we don't know how involved Hydra were in Avengers Assemble, it should be noted that the Battle of New York allowed them to;
- Obtain Loki's scepter,
- Justify the creation of Operation INSIGHT,
- (Almost) kill Nick Fury and Maria Hill, and
- (Almost) kill all of the Avengers.
Even if it turns out that the highly trained soldiers that accompanied Loki in Avengers Assemble weren't Hydra goons (and I believe that they were), the reveal that one of the members of the World Security Council at the time was part of Hydra indicates to me that they had at least some hand in what happened.
Edit 19/11/2015: In Agents of SHIELD season 3 episode 8 "Many Heads, One Tail";
We learn that Hydra is significantly older than previously thought - they have been active using one name or another for hundreds of years, and their ultimate goal is to bring an ancient Inhuman back to Earth so that it can rule the world.
It seems worth pointing out that the experimentation on the Tesseract (which we know to be the Space Gem) in Avengers Assemble by SHIELD (which we now know to be infiltrated at a high level by Hydra at the time) could be seen as a way for them to try and harness the power of the Space Gem in order to fulfill what we now know to be their ultimate goal. This would then explain why they decided to work with Loki - he is the only person that they have ever heard of being able to control and use the Tesseract.