It seems that you understand uses of "excuse me" pretty well. When we say "excuse me," it literally means "please forgive me for bothering you," or "please forgive me for occupying your time."
You can say "excuse me" when you don't understand what someone says and want the person to repeat it. It's like saying "I'm sorry to make you repeat yourself, but I didn't understand."
Example:
A: "It's a beautiful day!"
B: "Excuse me?"
A: "I said it's a beautiful day!"
If you need to talk to someone who you don't know, or someone who is busy doing something else, you can also say "excuse me." It's like saying "I don't mean to bother you, but I need to talk to you."
Example:
You're at the store to buy bread, but you can't find it. You see an employee and you say:
"Excuse me, where is the bread?"
If you accidentally do something to offend someone, you can say "excuse me" sometimes too. For instance, burping is considered rude in many countries, so if you burp, it's polite to say "excuse me." It tells the people around you that you don't want to be rude.
Sometimes people also use this phrase sarcastically when they think people are criticizing them unfairly.
Example:
A: "Why haven't you fixed the table? I asked you to do it last week!"
B: "Well, excuse me, but I have other projects too."
When people use it sarcastically, the syllable "cuse" is usually stressed harder or lengthened. "Ex-CUUUUSE me." You can hear examples of that usage in this video:
http://www.youtube.com/watch?v=FPxY8lpYAUM
I hope all this helps you understand "excuse me" a little better. If you have anymore questions, feel free to ask.