The recent release of Avengers' Trailer reminds me of an old question which has puzzled me for long. What is the difference between avenge and revenge? The translations in my language (Mandarin) for the two words are exactly the same.
Jeremy's answer that revenge is for the self and avenge is for others is often true, particularly in general usage, but isn't necessarily so.
It is true that one avenges a separate object indicated in the sentence, but that object could be an actual object (which might stand in for the self), as opposed to another individual.
You might certainly avenge your friend.
But you could just as easily avenge your honor.
In the second case, avenge is clearly an action undertaken for the self.
What distinction remains outside of grammatical usage (take revenge versus avenge someone/something) is morally tinged.
Revenge is typically displayed as an act of passion that offers the original victim catharsis but may not be the correct thing to do (in fact, may be entirely unjustifiable).
To avenge, on the other hand, is more about restoring balance and enacting justice.
Of course, much of the difference lies in the perspective of the speaker; is the slight imagined or grave? Is punishment merited, and if so, who should mete it out? Etc.
While the actions associated with them are the same, the motivations are not. They both mean to do something bad to someone because they already did something bad.
When you take revenge, you hurt someone who hurt you.
When you avenge someone, you hurt someone who hurt someone else.
Revenge is necessarily selfish; you are hurting the person who hurt you. Avenging can be honorable; you are seeking to settle the score with someone who hurt someone else.
If someone attacked you in the street, you might take revenge on them by finding them and hurting them back.
If someone attacked your friend in the street, you might avenge your friend by finding that someone and hurting them back.
Apart from avenge being a verb and revenge usually being a noun, my school thought sees avenge as a retaliation of a loved one on others or yourself while revenge is retaliation of oneself on others.