Or: Drink along to American college movies. Every time someone says "frat", "fraternity", "baseball", "football", or (by the end) any particularly American word, you drink.
The only down side to the LotR drinking game is that it takes a 3 hour slice from your life.
The other variant I've heard of is that everyone takes a character's name out of a hat, and every time that character is seen on screen or mentioned by name that person drinks. Everyone drinks whenever the Ring is mentioned.