Praise be to Allah.
Performing prayers at the right time is a trust and an obligation, because Allah says (interpretation of the meaning):
"Verily, al-Salaat (the prayer) is enjoined on the believers at fixed hours." [al-Nisaa' 4:103].
Delaying the prayer past its appointed time is a grave major sin, as Allah says (interpretation of the meaning):
"So woe unto those performers of salaat (prayers) (hypocrites), who delay their salaat from their stated fixed times." [al-Maa'oon 107:4-5]
Some scholars state that the person who deliberately misses one prayer and leaves it until the appointed time is over, with no excuse, is a kaafir. Claiming that one cannot find a place to pray is not a valid excuse, because either one is living on the face of the earth or not, and if one is living on the face of the earth, the Prophet (peace and blessings of Allah be upon him) said: "The (whole) earth has been made a mosque (or a place of prayer) and a means of purification for me, so wherever a man of my ummah may be when the time for prayer comes, let him pray." (Reported by al-Bukhaari, al-Fath, no. 335)
According to a report narrated by Muslim, he said: "The (whole) earth has been made good for me, a means of purification and a mosque (or place of prayer); so wherever a man may be when the time for prayer comes, let him pray wherever he is." (Saheeh Muslim, no. 521)
The entire world is a suitable place to prostrate oneself; the scholars have made no exceptions except very few, such as graveyards and lavatories. Wherever a Muslim is when the time for prayer comes, he should pray: in a mosque, if possible, or else in a hallway or park, on a sidewalk or in a parking lot, or in a corner of a store. Even if one can find no other place than a church, it is permissible to pray in it.
As far as praying on board means of transportation is concerned, then it is possible to pray there so long as the necessary conditions of prayer are fulfilled, or else one can wait until one gets out of the vehicle. If waiting means that the time for the prayer will pass, then you should pray in the best way that you can. Let us assume, for example, that you are in a car or train where there is no place to pray, you cannot stop and pray at the side of the road, and the time for that prayer is running out. In such a situation, the Muslim should pray in the best way that he can, even if he is sitting in his seat and even if he is not facing the qiblah, because Allah says (interpretation of the meaning): "So keep your duty to Allah and fear Him as much as you can" [al-Taghaabun 64:16], and because the Prophet (peace and blessings of Allah be upon him) said: "If I have commanded you to do something, do as much of it as you can." (Reported by al-Bukhaari, al-Fath, no. 7288)
An exception to be above is naafil (supererogatory) prayers offered when riding a camel, which is permissible even if one cannot get down or if one is not facing the qiblah. This is known from the report of Ibn 'Umar, who said: "The Prophet (peace and blessings of Allah be upon him) used to pray when travelling on his camel, no matter which direction it was facing, and he would gesture with his head to indicate the movements of the night prayer, apart from the obligatory prayers, and he would pray witr on his camel too." (Reported by al-Bukhari, 945)
Ibn 'Umar (may Allah be pleased with him) said: "The Prophet (peace and blessings of Allah be upon him) used to pray voluntary (nafl) prayers when riding on his camel, no matter what direction it was facing, when he came from Makkah to Madeenah." Then Ibn 'Umar recited this aayah (interpretation of the meaning): "And to Allah belong the east and the west, so wherever you turn yourselves or your faces, there is the Face of Allah (and He is High above, over His Throne)" [al-Baqarah 2:115]
Ibn 'Umar said: "It was concerning this that this aayah was revealed." (Reported by al-Tirmidhi, 2883; he said, this is a saheeh hasan hadeeth)
We should not forget to point out here that Muslims living in non-Muslim countries sometimes delay or abandon their prayers for another, completely different, reason, which is that they feel too embarrassed to pray in front of the kuffaar in public or open places, or they are afraid that they will make fun of them and regard them as odd. This is a serious mistake. How can a Muslim feel embarrassed about proclaiming the truth and worshipping openly, hastening to fulfil the command of Allah at the time when Allah has said it is to be done? This matter has been dealt with in a similar question on this website (see question # 980
). We ask Allah to help us all to remember Him, to be grateful to Him and to worship Him properly.