Hadith about belief.

Bukhari :: Book 1 :: Volume 2 :: Hadith 24

Narrated Ibn 'Umar:

Allah's Apostle said: "I have been ordered (by Allah) to fight against the people until they testify that none has the right to be worshipped but Allah and that Muhammad is Allah's Apostle, and offer the prayers perfectly and give the obligatory charity, so if they perform a that, then they save their lives an property from me except for Islamic laws and then their reckoning (accounts) will be done by Allah."

Bukhari :: Book 1 :: Volume 2 :: Hadith 25

Narrated Abu Huraira:

Allah's Apostle was asked, "What is the best deed?" He replied, "To believe in Allah and His Apostle (Muhammad). The questioner then asked, "What is the next (in goodness)? He replied, "To participate in Jihad (religious fighting) in Allah's Cause." The questioner again asked, "What is the next (in goodness)?" He replied, "To perform Hajj (Pilgrim age to Mecca) 'Mubrur, (which is accepted by Allah and is performed with the intention of seeking Allah's pleasure only and not to show off and without committing a sin and in accordance with the traditions of the Prophet)."

Bukhari :: Book 1 :: Volume 2 :: Hadith 26

Narrated Sa'd:

Allah's Apostle distributed (Zakat) amongst (a group of) people while I was sitting there but Allah's Apostle left a man whom I thought the best of the lot. I asked, "O Allah's Apostle! Why have you left that person? By Allah I regard him as a faithful believer." The Prophet commented: "Or merely a Muslim." I remained quiet for a while, but could not help repeating my question because of what I knew about him. And then asked Allah's Apostle, "Why have you left so and so? By Allah! He is a faithful believer." The Prophet again said, "Or merely a Muslim." And I could not help repeating my question because of what I knew about him. Then the Prophet said, "O Sa'd! I give to a person while another is dearer to me, for fear that he might be thrown on his face in the Fire by Allah."