Adding to Jaysalos answer, Roman law (and not laws) was also rediscovered around the XIIth century in Europe. And soon after directly applied in south France, cities-states of what we called today Italy, provinces of Prussia, Austria, Switzerland and Spane. In north France and United Kingdom, officially, custom law and King's decisions were applied. But in reality, roman law exercised a very strong influence on them too. For example, the very rules of loan contracts or rent were extracted from roman texts.

The most obvious answer would be The Catholic Church and The Orthodox Church. If we take another definition of institution “an established law, practice or custom” then we can start naming a great number of things. Roman architecture and philosophy are still very relevant today not to mention Latin is still used daily world wide in scientific fields and in many sayings we have even in English. Roman law is the foundation of civil law that is the most commonly used form of law we have today. And while obviously many of these things have evolved or died from their original form over the past 2,000 or so years it’s tough to look at almost any aspect Western civilization and not see the finger prints of the old Roman institutions.