Allah wants ease for his servants and not hardship. So, there are some people for whom the Fast during Ramadan is not obligatory. Among those:

1- The traveler:

The traveler can choose between fasting or not. Allah said, which means:
{… And whoever of you is sick or on a journey, the same number [of days which one did not observe fasting must be made up] from other days. Allah desires for you ease; He desires not hardship for you…} [Quran 2:185]

Hamza Ibn 'Amr Al-Aslamee, who used to fast frequently asked the Messenger (sallallahu alayhe wa sallam): "Do I have to fast if I am travelling?" The Messenger said: "Fast if you wish or break the fast if you wish." [Al-Bukhari and Muslim]

Anas Ibn Malik said: "I was travelling with the Messenger of Allah during Ramadan, and those who fasted did not blame those who did not fast, and neither did those who did not fast blame those who fasted." [Al-Bukhari and Muslim]

The above two hadeeths indicate that there is a choice for the traveller between fasting and leaving off the fast but does not indicate which of the two ways is better. However, from the following hadeeth we can deduce that it is better not to fast when on a journey. The Messenger said: "Verily Allah loves that His concessions be accepted just as He hates to be disobeyed."[Ahmad and Ibn Hibban].

According to Imam Ahmed (May Allah's Mercy be upon him), not to fast on a journey is the better choice for the one who finds no hardship in fasting. However, the majority of the scholars say that fasting is better for the traveler if there is no hardship because it is a clearance of one's soul of Allah's debts, but if there is any hardship for him to fast during his travel, then it is highly preferable for him not to fast.

It must be noted that it is not righteousness for a weak traveler to fast as the messenger said: "It is not righteousness that you fast while on a journey." [Al-Bukhari and Muslim]

Note: Some people think that because the ways of travelling have become easier, this ruling of not fasting on a journey no longer applies any longer. This is a serious misconception, because Allah devised His Laws for all times and places: "Your Lord is Never Forgetful."

2- The Sick person:

Because of His Mercy, Allah has allowed for the sick person not to fast, to make it easy for him. The type of sickness that allows a sick person not to fast is that which, if he fasts, would cause him harm or prolong the illness. And Allah knows best.

3- States of Menses or Post-childbirth Bleeding:

The scholars have unanimously agreed that it is not allowed for the woman who is having her menstrual period and the woman who is affected with post-childbirth bleeding to fast. They should break their fast and make up the days later. They also agree that if they fast then no rewards would occur to them.

4- The Old Man and Old Woman and those with chronic Diseases:

Mujahid narrated that Ibn Abbas recited: {…And as for those who can fast (with difficulty e.g. an old man), they have to feed a poor person (for every day)….} [Quran 2:184], and then he said: "That refers to the old person who is not able to fast. He must feed a poor person a half saa' (two handfuls) of grains for every day missed."

Abu Hurairah said: "Whoever reaches old age and is not able to fast in Ramadan, then for every day he must give away one mudd ( a handful) of wheat." [Ad-Daarimi]

5- The pregnant and the breast-feeding women:

Allah's great mercy towards the weak is His concession for them not to fast. Included in this category are the pregnant and breast-feeding women. Then they must make up the same number of days they have missed whenever they would be able to do so.

Anas Ibn Malik said: "The horses of the Messenger of Allah came towards us, so I came up to the Messenger of Allah and I found him eating. He said: "Come closer and eat." I said: "I am fasting." He said: "Come closer and let me tell you about fasting. Indeed Allah has reduced the Salat (prayer) for the traveler to the half, and has removed the burden of the fasting from the pregnant and the breast-feeding woman…" [At-Tirmidhi, An-Nasaai]