Do not remain nameless to yourself - it is too sad a way to be. Know your place in the world and evaluate yourself fairly, not in terms of the naive ideals of your own youth, nor in terms of what you erroneously imagine your teacher's ideals are. - Richard Feynman
Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard P. Feynman (2005)

The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. ...No problem is too small or too trivial if we can really do something about it. - Richard Feynman
Perfectly Reasonable Deviations from the Beaten Track: The Letters of Richard P. Feynman (2005)

Science alone of all the subjects contains within itself the lesson of the danger of belief in the infallibility of the greatest teachers in the preceding generation...Learn from science that you must doubt the experts. As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts. - Richard Feynman 
The pleasure of Finding Things Out: The best short works of Richard Feynman, P.186-187.

I can live with doubt and uncertainty and not knowing. I think it's much more interesting to live not knowing than have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of certainty about different things, but not absolutely sure of anything, and many things I don't know anything about... But I don't have to know an answer, I don't feel frightened by not knowing things, by being lost in the mysterious universe without having any purpose, which is the way it really is as far as I can tell, possibly. It doesn't frighten me. - Richard Feynman
http://www.youtube.com/watch?v=_MmpUWEW6Is

You can know the name of a bird in all languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird...So let's look at the bird and see what it's doing - that's what counts. I learned very early the difference between knowing the name of something and knowing something. - Richard Feynman

I think I can safely say nobody understands quantum mechanics - Richard Feynman

God was invented to explain mystery. God is always invented to explain those things that you do not understand. Now, when you finally discover how something works, you get some laws which you're taking away from God; you don't need him anymore. But you need him for the other mysteries. So therefore you leave him to create the universe because we haven't figured that out yet; you need him for understanding those things which you don't believe the laws will explain, such as consciousness, or why you only live to a certain length of time — life and death — stuff like that. God is always associated with those things that you do not understand. Therefore I don't think that the laws can be considered to be like God because they have been figured out.- Richard Feynman