Monash University Law Faculty and Law Students' Society run a number of moots:
"Jessup is the world's largest moot court competition, with participants from over 550 law schools in more than 80 countries. The Competition is a simulation of a fictional dispute between countries before the International Court of Justice, the judicial organ of the United Nations." (Jessup website)
The Philip C. Jessup Library (Hein Online) contains award winning memorials, problems, bench memoranda and official rules, as well as articles from:
The Law Library holds DVDs of the final rounds of the winning teams from 2000 to the current year and print versions of the memorials.
Researching international law [PDF] (Jessup Guide)
"The Willem C. Vis International Commercial Arbitration Moot is a competition for law students. Students from all countries are eligible. The Moot involves a dispute arising out of a contract of sale between two countries that are party to the United Nations Convention on Contracts for the International Sale of Goods." (from the website)