Shortening the prayers when travelling is a confirmed Sunnah

Shortening the prayers when travelling is a confirmed sunnah
that one should not forsake, according to the consensus of the imams
(leading scholars), apart from what is narrated from ash-Shaafa‘i in one of
his two opinions, that offering the prayers in full is preferable. However
the correct view in his madhhab is that shortening the prayers is
preferable. 

See: al-Majmoo‘ by an-Nawawi, 4/218-223 

The view that shortening the prayers is preferable is
supported by the fact that the Prophet (blessings and peace of Allah be upon
him) shortened the prayers in all of his journeys, and there is no saheeh
report to indicate that he ever offered the prayer in full when he was
travelling. 

Anas ibn Maalik (may Allah be pleased with him) said: We went
out with the Prophet (blessings and peace of Allah be upon him) from Madinah
to Makkah, and he offered his prayers with two rak‘ahs every time until we
returned to Madinah.

Narrated by al-Bukhaari, 1081; Muslim, 724. 

Ibn ‘Umar (may Allah be pleased with him) said: I accompanied
the Messenger of Allah (blessings and peace of Allah be upon him) and during
the journey he did not pray more than two rak’ahs (in any prayer), and Abu
Bakr, ‘Umar and ‘Uthmaan (may Allah be pleased with them) did likewise.

Narrated by al-Bukhaari, 1102; Muslim, 689 

This refers to the beginning of ‘Uthmaan’s caliphate; at the
end of his caliphate, ‘Uthmaan (may Allah be pleased with him) used to offer
the prayers in full (when travelling). 

When ‘Abdullah ibn Mas‘ood (may Allah be pleased with him)
heard that ‘Uthmaan ibn ‘Affaan (may Allah be pleased with him) was offering
the prayers with four rak‘ahs in Mina, he said:
Inna Lillaahi wa inna ilayhi raaji ‘oon
(Verily to Allah we
belong and verily to Him is our return). I prayed two rak ‘ahs with the
Messenger of Allah (blessings and peace of Allah be upon him) in Mina, and I
prayed two rak ‘ahs with Abu Bakr al-Siddeeq in Mina, and I prayed two rak
‘ahs with ‘Umar ibn al-Khattaab in Mina. 

Narrated by al-Bukhaari, 1084; Muslim, 695 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: 

It is makrooh to offer the prayers in full when travelling.
Ahmad said: I do not like it. It was narrated from Ahmad that he would not
comment on whether offering four rak‘ahs would be valid. There is no sound
report to indicate that any of the Sahaabah (may Allah be pleased with them)
used to pray with four rak‘ahs when travelling at the time of the Prophet
(blessings and peace of Allah be upon him). The hadeeth narrated from
‘Aa’ishah that suggests something to the contrary cannot be taken as
evidence.

End quote from al-Ikhtiyaaraat, p. 32 

Ibn al-Qayyim (may Allah be pleased with him) said in Zaad
al-Ma‘aad, 1/464: 

The Prophet (blessings and peace of Allah be upon him) used
to shorten the four-rak‘ah prayers, praying them with two rak‘ahs, from the
time he set out travelling until he returned to Madinah. There is no sound
report from him to suggest that he ever offered the four-rak‘ah prayers in
full whilst travelling. 

With regard to the hadeeth of ‘Aa’ishah, according to which
the Prophet (blessings and peace of Allah be upon him) used to shorten the
prayers and offer them in full when travelling, and that he used to not fast
and fast, it is not saheeh. I heard Shaykh al-Islam Ibn Taymiyah say: This
is a lie against the Messenger of Allah (blessings and peace of Allah be
upon him). End quote. 

It was narrated that the Prophet (blessings and peace of
Allah be upon him) used to shorten the prayers but ‘Aa’ishah would offer
them in full, and he might not fast one day but she would fast. 

Our Shaykh Ibn Taymiyah said: This is false. The Mother of
the Believers would not go against the Messenger of Allah (blessings and
peace of Allah be upon him) and all his companions, and pray differently
from them. End quote. 

Rather some of the imams, such as Imam Abu Haneefah and Ibn
Hazm (may Allah have mercy on them) were of the view that shortening the
prayers when travelling is obligatory, and it is not permissible to offer
them in full. 

However, the correct opinion is that of the majority of
scholars, that shortening the prayers is Sunnah and is preferable, and is
not obligatory. That is supported by the fact that ‘Uthmaan and ‘Aa’ishah
(may Allah be pleased with them) offered prayers in full when travelling. If
shortening the prayers when travelling was obligatory, they would not have
offered them in full. The Sahaabah followed ‘Uthmaan (may Allah be pleased
with all of them) in offering the prayers in full in Mina; if offering the
prayers in full was haraam, they would not have followed him in that. 

Imam ash-Shaafa‘i (may Allah have mercy on him) said: If it
had been obligatory for the traveller to pray with two rak‘ahs, ‘Uthmaan,
‘Aa’ishah and Ibn Mas‘ood would not have offered the prayers in full, and it
would not have been permissible for a traveller to offer the prayers in full
when praying with a resident who is not travelling.

End quote from al-Umm, 1/159 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said in
ash-Sharh al-Mumti‘, 4/358-362: 

Some of the scholars said that offering the prayers in full
(when travelling) is makrooh (disliked), because this is contrary to the
regular, ongoing practice of the Prophet (blessings and peace of Allah be
upon him), as the Messenger (blessings and peace of Allah be upon him) never
offered the prayer in full when travelling, and he said: “Pray as you have
seen me praying.” This is the view favoured by Shaykh al-Islam Ibn Taymiyah
(may Allah have mercy on him) and it is a strong view; in fact it may be the
strongest of the opinions. 

Some of the scholars said that shortening the prayers is
obligatory and that the one who offers the prayer in full is sinning. 

What seems to me to be most correct is that offering the
prayers in full (when travelling) is makrooh, not haraam, and that the one
who offers the prayer in full is not sinning. This is from a theoretical
point of view. 

But from a practical point of view, is it befitting for a
person to do something when he fears that he may be sinning thereby? 

It is not appropriate conduct; rather you
should do what is Sunnah, because that is better for your spiritual
wellbeing, even if it is permissible for you to do something contrary to
that. End quote. 

Based on that, it is preferable for the
traveller to shorten his prayers, but he does not have the right to refrain
from offering the prayer in congregation for the sake of shortening the
prayer; rather he must offer prayers in congregation. If the imam is a
resident (not travelling), he must offer the prayer in full with him, and if
he is travelling, he must shorten the prayer with him. 

This has been discussed previously in the
answers to questions no. 26186
and 40299.