What are the values represented in the poem "If" by Rudyard Kipling?

The values of the poem are old-fashioned, conservative, and even aristocratic. Kipling comes by all these values honestly.  Recall that he was born in British India and spent parts of his life in England, America, and South Africa.  He was an educated aristocrat who achieved fame and influence in his life.  For more about Kipling's family and biography, see the link below.  What I have called "aristocratic" values include courage, risk-taking, self-discipline, leadership, the "stiff upper lip," hard work, taking responsibility, and stoicism.
Besides aristocratic values, the poem also has a sub-theme of democratic values.  Kipling was a warm-hearted man who loved, not hated, India, unlike our stereotype of the colonial British.  What I have called "democratic" values include humility, respect for everyone, not returning evil for evil, and egalitarianism.
Here is a list of values with quotes from the poem:

courage/fortitude: "If you can force your heart and nerve and sinew ..."

risk-taking: "If you can make one heap of all your winnings ..."

self-discipline: All the behaviors described in the poem require self-discipline.

leadership: "If you can keep your head ..." and "If you can bear to hear the truth you've spoken ..." both describe situations usually encountered by leaders.  There is also "talk with crowds ... walk with Kings" which seem to assume a person with some power and influence.

the "stiff upper lip": "And never breathe a word about your loss." This value is less about having no feelings than about not displaying your feelings publicly nor complaining about your losses and hardships.   Contrast it with stoicism, below, which is not quite the same thing.

hard work: "If you can fill the unforgiving minute ..." 

taking responsibility: "If you can bear to hear the truth you've spoken ..." is about sticking to your policies rather than blame-shifting.  "Stoop to build 'em up with worn-out tools" is about starting over when your work has had a setback through no fault of your own.  In this case, the person is taking responsibility for work that is theirs to do, although the need for the work is someone else's fault.

stoicism: Stoicism is a Greek value that involves actually not caring too much about any one thing or person. It is a cold, self-protective value, and it clashes somewhat with the warm, democratic values below.  "If you can meet with Triumph and Disaster ..." implies that a person should be unmoved no matter what happens.  "If neither foes nor loving friends can hurt you,/If all men count with you, but none too much" is another stoic value.  The idea is that we should not care about another person enough that mistreatment from them could possibly shake our inner calm.  I doubt that, in real life, Kipling achieved this state in its pure form.  

humility: "But make allowance for their doubting too."  This line calls us to be confident, but still able to recognize that we can be wrong.  Also, is is impossible to "not return evil for evil" without being humble.

respect for everyone: "If you can talk with crowds and keep your virtue,/Or walk with Kings -- nor lose the common touch"

not returning evil for evil: "Or being hated, don't give way to hating"  This value was most clearly articulated by Jesus.

egalitarianism: "And yet don't look too good, nor talk too wise."  Egalitarians always take care not to look better than other people, not to stand out from the crowd. 
It is amazing the number of values that Kipling sketched in this poem. Trying to live up to it could take a lifetime.
 
 
 
http://www.kiplingsociety.co.uk/kip_fra.htm