I find the following two points especially relevant for me:
a) "If you can think - and not make thoughts your aim";
b) "If all men count with you, but none too much."
Both of these lines speak to particular weaknesses that I have.
I tend to think a lot and to read a lot of books (that's how I'm able to answer questions on enotes.com). Sometimes all that thinking and reading can get in the way of getting "real" things done, little things like working, cleaning up, exercising, calling Mom, etc. So I appreciate Kipling's advice to think but not to "make thoughts your aim."
Another weakness I have is that I can't really decide if I care what other people think about me or not. Sometimes I brag that I don't give a damn about what anyone says, but deep down I know that I want to be accepted by others. I think that Kipling strikes a good balance when he says that all men should "count with you, but none too much."
This is a matter of opinion, and I imagine that different answers will present itself. For my bet, I am partial to the two moments in the poem where the speaker addresses the ideas of not making dreams "your master" and "never breath a word about your loss." I think these are extremely powerful because they have proven to have personal relevance to me. The idea of being in control of dreams and not allowing them to fully drive the individual to destructive ends is quite persuasive in terms of advice given to another. At the same time, I also like the idea of being able to handle, accept, and work through the idea of loss. This is something that is very much applicable to anyone, but the idea of keeping it in one's mind and not using it as a part of a victimization methodology is extremely powerful. Keeping a sense of stoic dignity about one's losses is extremely compelling advice.
One of the best points in this is the idea that you should be able to dream but not to let the dreams be your master. This is saying that you have to have goals, but you should not think about them so much that you lose sight of what you are doing now. This makes sense because you have to be practical as well as ambitious.
A second point is that you should be able to keep trying even when all seems lost -- to force yourself to keep going when heart and nerve and sinew are gone. It is very important never to give up because you never know what will be possible if you keep trying.