I'm thinking of ones I've been somewhat familiar with for much of my life (for instance, John F. Kennedy's and Lincoln's second), ones I've become more familiar with recently (such as Lincoln's first), and one I just looked at today (Jefferson's first--though I have heard one sentence from it before).
Let's proceed in chronological order, starting with Jefferson's first inaugural address (see http://en.wikisource.org/wiki/Thomas_Jefferson%27s_First_Inaugural_Address for a transcript). Here, commenting on the very rough political campaign through which the nation had suffered, is a passage that has quickly become one of my favorites, especially the part I've highlighted:
During the contest of opinion through which we have passed the animation of discussions and of exertions has sometimes worn an aspect which might impose on strangers unused to think freely and to speak and to write what they think; but this being now decided by the voice of the nation, announced according to the rules of the Constitution, all will, of course, arrange themselves under the will of the law, and unite in common efforts for the common good. All, too, will bear in mind this sacred principle, that though the will of the majority is in all cases to prevail, that will to be rightful must be reasonable; that the minority possess their equal rights, which equal law must protect, and to violate would be oppression. Let us, then, fellow-citizens, unite with one heart and one mind. Let us restore to social intercourse that harmony and affection without which liberty and even life itself are but dreary things. And let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions. . . . [E]very difference of opinion is not a difference of principle. We have called by different names brethren of the same principle. We are all Republicans, we are all Federalists.I had heard this last sentence before, but not with what leads up to it.
Lincoln's first inaugural address is remarkable, responding temperately and even affectionately to the storm of anger and suspicion his election had provoked. (See http://avalon.law.yale.edu/19th_century/lincoln1.asp and http://en.wikipedia.org/wiki/Abraham_Lincoln's_first_inaugural_address.) Here are some selections:
Why should there not be a patient confidence in the ultimate justice of the people? Is there any better or equal hope in the world? In our present differences, is either party without faith of being in the right? If the Almighty Ruler of Nations, with His eternal truth and justice, be on your side of the North, or on yours of the South, that truth and that justice will surely prevail by the judgment of this great tribunal of the American people. . . .
In your hands, my dissatisfied fellow-countrymen, and not in mine, is the momentous issue of civil war. The Government will not assail you. You can have no conflict without being yourselves the aggressors. You have no oath registered in heaven to destroy the Government, while I shall have the most solemn one to "preserve, protect, and defend it."
I am loath to close. We are not enemies, but friends. We must not be enemies. Though passion may have strained it must not break our bonds of affection. The mystic chords of memory, stretching from every battlefield and patriot grave to every living heart and hearthstone all over this broad land, will yet swell the chorus of the Union, when again touched, as surely they will be, by the better angels of our nature.
And of course, Lincoln's second inaugural address is justly famous, one of history's most moving and eloquent expressions of humility and compassion (see http://avalon.law.yale.edu/19th_century/lincoln2.asp and http://en.wikipedia.org/wiki/Lincoln%27s_second_inaugural_address):
On the occasion corresponding to this four years ago all thoughts were anxiously directed to an impending civil war. . . . Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish, and the war came.
. . . Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible and pray to the same God, and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God's assistance in wringing their bread from the sweat of other men's faces, but let us judge not, that we be not judged. The prayers of both could not be answered. That of neither has been answered fully. The Almighty has His own purposes. "Woe unto the world because of offenses; for it must needs be that offenses come, but woe to that man by whom the offense cometh." If we shall suppose that American slavery is one of those offenses which, in the providence of God, must needs come, but which, having continued through His appointed time, He now wills to remove, and that He gives to both North and South this terrible war as the woe due to those by whom the offense came, shall we discern therein any departure from those divine attributes which the believers in a living God always ascribe to Him? Fondly do we hope, fervently do we pray, that this mighty scourge of war may speedily pass away. Yet, if God wills that it continue until all the wealth piled by the bondsman's two hundred and fifty years of unrequited toil shall be sunk, and until every drop of blood drawn with the lash shall be paid by another drawn with the sword, as was said three thousand years ago, so still it must be said "the judgments of the Lord are true and righteous altogether."
With malice toward none, with charity for all, with firmness in the right as God gives us to see the right, let us strive on to finish the work we are in, to bind up the nation's wounds, to care for him who shall have borne the battle and for his widow and his orphan, to do all which may achieve and cherish a just and lasting peace among ourselves and with all nations.
John F. Kennedy's inaugural address fall short of this last one of Lincoln's, yet is one of the most memorable of the 57 or so that have been delivered over the past two hundred plus years. (See http://avalon.law.yale.edu/20th_century/kennedy.asp and http://en.wikipedia.org/wiki/John_F._Kennedy%27s_Inaugural_Address --and listen at http://www.americanrhetoric.com/speeches/jfkinaugural.htm.) Some of my favorite passages:
Let the word go forth from this time and place, to friend and foe alike, that the torch has been passed to a new generation of Americans. . . . Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe, in order to assure the survival and the success of liberty.
. . .
So let us begin anew--remembering on both sides that civility is not a sign of weakness, and sincerity is always subject to proof. Let us never negotiate out of fear. But let us never fear to negotiate.
Let both sides explore what problems unite us instead of belaboring those problems which divide us.
. . .
Let both sides unite to heed in all corners of the earth the command of Isaiah--to "undo the heavy burdens ... and to let the oppressed go free."
. . .
Now the trumpet summons us again--not as a call to bear arms, though arms we need; not as a call to battle, though embattled we are--but a call to bear the burden of a long twilight struggle, year in and year out, "rejoicing in hope, patient in tribulation"--a struggle against the common enemies of man: tyranny, poverty, disease, and war itself.
And so, my fellow Americans: ask not what your country can do for you--ask what you can do for your country.
My fellow citizens of the world: ask not what America will do for you, but what together we can do for the freedom of man.
Finally, whether you are citizens of America or citizens of the world, ask of us the same high standards of strength and sacrifice which we ask of you. With a good conscience our only sure reward, with history the final judge of our deeds, let us go forth to lead the land we love, asking His blessing and His help, but knowing that here on earth God's work must truly be our own.
All of these passages take on much of their meaning from the times in which they were first spoken. But they also take on meaning from the character of those who spoke them and from the connection we feel over time with the speakers and their audiences and the generous desires that moved them to speak and listen.