One of the oldest recorded character conflicts is the struggle between men. Ancient literary masterpieces, such as the Iliad, have portrayed the ongoing struggle between humans for supremacy. Your character doesn't need to participate in an epic battle to display this type of conflict, though. Modern references to the struggle between men can manifest themselves in the adversarial relationship between a student and a bully. There are all sorts of different conflicts between men, though, not just physical altercations. For example, a character could compete against his neighbor for the "best lawn" award. The character's conflict would consist of preparing his lawn and constantly trying to best his neighbor's attempts.
The struggle for survival against the elements is a common conflict a character can face. Notable references to man versus nature include the 2009 film "2012" or "Walden," written by Thoreau. It's inspirational to think of a character persevering over the power of nature and surviving despite the odds. Any time you read about a person facing off against an animal or suffering through a natural disaster, it's an example of man versus nature. Sometimes man triumphs, and sometimes nature is the victor.
Internal conflict can be one of the most riveting types to observe. Internal conflict occurs when a character has two markedly contrasting views within his mind. For example, if a soldier has strong feelings against taking a life but his work requires him to do so, he can undergo a severe internal struggle. His morals conflict with his sense of duty, leaving him to agonize over his choice until either his beliefs or his responsibility to the military wins the struggle.
When you pit a character against aliens, deities or spirits, you are pitting her against a supernatural source. Unlike the man versus man conflict, the opponent of the character is either a supernatural force without a concrete form or an extraterrestrial life form. A conflict with a supernatural force opens up a whole host of opportunities for your character's storyline. For example, if Odysseus didn't anger the gods in the Odyssey, he would have sailed back to Ithaca unimpeded. Instead, he had to travel through Hell, suffer with his crew members and experience extraordinary phenomena because of his conflict with a supernatural force. No man could create such trials for Odysseus without having supernatural powers.