Question: I've thought about my protagonist's main goal and I've tried to keep in mind that the villain will want to prevent the main character from achieving this goal. However, I'm having a hard time figuring out what motivates my antagonist. It seems that things such as power, wealth, and greed are very cliche motivations. Any advice?
It does depend what type of story you are writing.
A classic "villain" has three main characteristics.
1. He (or she) is the antagonist, who tries to prevent the Story Goal from being achieved.
2. He is the impact character, who represents the opposite way of being/doing things to the hero. The hero can define himself by looking at the villain and saying, "I'm not like him because..."
3. He is someone the reader dislikes.
Now, this classic villain character has been done many times, as you say, and still keeps appearing in stories - particularly genre fiction. Think of it as a shortcut when you want to focus on the adventure (as in comic books, action films, etc.) rather than the characters.
However, it can be interesting to do variations on this classic character.
For instance, the reason so many villains have greed for wealth or power is because seeking these things while disregarding (or at the expense of) the rights and welfare of others is the classic definition of evil. It makes the reader dislike the villain. Sometimes, you can create a villain who is more sympathetic. He could be trying to do the wrong thing for the right reason. Think of comic book characters like Catwoman, who commits crimes in order to champion the environment. Or you can have a villain who is seeking redress of some imagined wrong that was done to him. He may be going about
things in the wrong way, but the reader can understand his motivation. Readers often see moral ambiguity as more realistic.
You could also look for other ways to make the antagonist unlikeable. Maybe he is cruel for no reason (a psychopath or sociopath). Maybe he causes trouble just for fun. Maybe his lust is for the hero's girlfriend, or some other object of desire. Maybe he has bad manners.
As for opposing the Story Goal, there are many reasons why the protagonist and antagonist find themselves in opposition. Just as in a war, each side feels justified, you can create an antagonist who sees opposing the Story Goal as a good deed. He may simply have a different perspective. Or he may feel threatened in some way if the goal is achieved.
Regarding the third quality, often it is more interesting to assign the role of impact character to someone other than the antagonist. If the antagonist is the impact character, then the main character must stick to his values, his way of doing things, in order to achieve the goal.
But in most stories today, the main character resolves his inner conflict by changing and adopting the impact character's values. That's a problem if the impact character is the villain, so usually you make the impact character someone else, someone the main character can learn from in order to defeat the villain.
Of course, you can make the villain the impact character, in which case the story becomes a very personal conflict between the hero and villain in which the hero is sorely tempted to become like the villain and must struggle to stay true to a different set of values. Or you can write a tragedy in which the main character becomes like the villain and suffers the consequences.