I'll start of with a few...
You can die for your country, I'm gonna live for mine.
Anything in life worth doing is worth overdoing. Moderation is for cowards.
There ain't nothing I can't do. No sky too high, no sea too rough, no muff too tough.
Pushing ourselves into those dark cold corners where the bad things live. Where the bad things fight.
Whatever it takes...Find an excuse to win.
Just a few I use when I finding it tough on Ten tors etc physically demanding and mentally due to pain.
History will be kind to me for I intend to write it.
Remember, regardless of the overwhelming opposition or adversity in your path, you always have the opportunity to overcome. It is your attitude that will determine the outcome.
"On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
-- Charles Babbage
I'm not sure if "inspiring" is the right term for why I like this quote, as with everything else in my life I'm sure that it has more to do with my ego than I care to acknowledge. The fact that people like this exist and have always existed, and that they look at me for answers to questions like this all the time does help me when I get to the point where I'm asking why I bother.
Not really ones that inspire me, but some favorite quotes:
"Men will never be free until the last king is strangled with the entrails of the last priest." - Denis Diderot
"He who fights with demons should see to it that he does not become one. When one gazes into the abyss, the abyss in turn gazes back into you." - Friedrich Nietzsche
"Nothing is impossible unless proven to be" - cleverbot
transcript -
cleverbot - I think you are confused about who you are.
me - That sounds philosophical.
cleverbot - Are you sure?
me - Yes. I am. Do you have any other philosophical ideas?
cleverbot - Nothing is impossible unless proven to be.
me - That is a very inspiring quote.
cleverbot - I know, you can use it if you want.
It's a motivational quotation from cleverbot, not science. Although, surely by that logic a simple rewording of the original quotation would reverse your statement and everything would be possible until proven not to be.