1) Relative Value
I've discussed the first two here and here. Directional funds are the most risky of the lot, as they involve taking massive bets on the direction of the market. Why do I call them massive bets as opposed to regular bets? Because they often involved a large amount of leverage, which magnifies both gains and losses.
As an example, if you invest $10 and achieve a 10% return, you'll have $11. However, if instead of just investing $10, you borrowed another $10, well that same 10% return would net you $12 (after paying the lender back), a return of 20% on your original $10. This amplifying of your gains will do the same for your losses as well.
Such hedge funds will take large long or short bets on equities, bonds, indexes, currencies or any derivatives. Many hedge funds of this nature also focus on emerging markets, as they are often less efficient due to lack of investor interest and information flow.