I kinda divide it into 2 categories. First is the great speeches from history such as the Gettysburg Address or the Kennedy Inaugural. The second is the ones seen 'live'. Obviously the ones that I saw live weigh heavier in my mind than the ones that I studied even though they may not be as important.
Of the ones that I saw live that stick out immediately, I'd have to say:
The Reagan Challenger Speech
The Reagan Tear Down This Wall
Bush 43 - Freedom and Fear (We will not tire, we will not falter, and we will not fail.)
Those are the speeches that really affected me. I can remember great lines from all 4 of those.
My favorite speech is Washington's Farewell address. I thought that was the best speech ever given by a president. I also love Lincoln's Gettysburg Address. Kennedy's Inaugural speech was very good also as were some of Reagan's. His speech at the 40th anniversary of D-Day and his Tear Down this Wall speech were very good. Some of Theodore Roosevelt's speeches were very good as well.
I like FDR's first inaugural address: the "only thing we have to fear is fear itself" speech. It was more than a simple statement of position, or move to grab political advantage or favor, but aimed straight at solving the problems of a failing economy by speaking of the opportunity and promise of the future. The speech is not likely the sole reason the economy turned around on more-or-less the day of FDR's inauguration, but I imagine it helped.
Eisenhower's speech denouncing the military industrial complex. Given who he was it was a remarkable thing for him to do. It might not have been the most accurate speech in terms of pertaining to the immediate situation when he was president, but I read it more as a warning to world leaders of the future, and what he said certainly rings true today.
Also the FDR's inaugural address...though enough people have mentioned that already.