Anything that an individual can trade and invest in, can be traded and invested in by a partnership or LLC. So narcotics, endangered animals, and human organs are out, but South African debt, Israeli real estate, and fine art are all possibilities.
Although you are stretching the definition of "hedge fund" with some things. Like a real estate partnership wouldn't really be considered a hedge fund, for example. When you say "hedge fund" most people think of exchange or investment bank traded securities and derivatives -- but like you say, it doesn't matter where they are traded and there are no rules saying what it can or can't be.