If a person denies the obligation of the fast, he becomes a disbeliever. Its obligatory status is confirmed in the Qur'aan and numerous ahaadeeth of the Prophet صلى الله عليه وسلم. 

As for the one who believes in the fast but does not fast, there is a hadeeth which states, 

عرى الإسلام وقواعد الدين ثلاثة عليهن أسس الإسلام من ترك واحدة منهن فهو بها كافر حلال الدم : شهادة أن لا إله إلا الله والصلاة المكتوبة وصوم رمضان 

"The bare essence of Islaam and the basics, upon which Islaam has been established, are three. Whoever leaves one of them becomes an unbeliever and his blood may legally be spilled. [These acts are:] Testifying that there is no God except Allaah, the obligatory prayers and the fast of Ramadhaan." 

This hadeeth was recorded by Abu Ya'la and ad-Dailami. Some scholars have called it hasan. However, the correct view seems to be that of Shaykh al-Albaani رحمه الله, that the hadeeth is weak. But, most likely, it seems that it is a statement of the Companion ibn 'Abbaas رضي الله عنهما and not that of the Prophet (peace be upon him). [1] 

Therefore, it cannot be considered an overriding proof in this matter, especially if there is no record that the other Companions رضي الله عنهم agreed with him on this point. 

However, a Companion coming to such a conclusion demonstrates the importance of this act of fasting. No scholar would make such a statement, not to speak of a Companion, unless that act was of great importance in Islaam. Although the majority and the strongest opinion is that such a person does not become a disbeliever, those Muslims who refuse to fast the month of Ramadhaan should consider ibn 'Abbaas' رضي الله عنهما statement very carefully as there is a likelihood that what he said is correct. 

Furthermore, Imaam adh-Dhahabi رحمه الله once wrote, 

"According to the established believers, anyone who leaves the fast of Ramadhaan without being sick is worse than a fornicator or an alcoholic. In fact, they doubt his Islaam and they suspect that he might be a zindeeq (renegade against Islam) and one of those who destroy Islaam." [2] [3] 

Notes: 

[1] See: Silsilat al-Ahaadeeth ad-Dha'eefah (Beirut: al-Maktab al-Islaami, 1398 A.H.), vol. 1, pp. 131-2. 

[2] Quoted in as-Sayyid Saabiq رحمه الله, Fiqh us-Sunnah, vol. 3, p. 111. 

[3] Shaykh Jamaluddin Zarabozo حفظه الله, Commentary on the Forty Hadith of al-Nawawi, vol. 1, pp. 319-320.

See also: Fasting the Month of Ramadaan