Why did the Romans decide that Jesus should die by crucifixion?

Pontius Pilate, the relevant Roman Governor gave sentence, against Roman justice to condemn Jesus Christ, allowing him to be crucified.

He did this due to the political pressure put upon him by the Jews. Normally Pilate was known as a tough and often uncompromising, (even cruel) ruler and so such an action, where he 'caved in' to pressure seems certainly out of character.

Two factors gave the Jews significant leverage over Pilate. Firstly Pilate was a friend of one Sejanus (executed in 31AD) who, as head of the Praetorian guard in Rome had been implicated in a plot against Caesar. This did not put Pilate in a strong position politically, He was a marked man as far as Caesar was concerned.

Secondly, the Jews had in the recent past won an important 'victory' over an intransigent Pilate. Pilate had placed some heathen 'votive shields' in the temple which grossly offended the Jews as idolatrous. Despite protestations he refused to remove them and so the Jews complained to Caesar. So incensed was he that he despatched an immediate reply to Pilate ordering their removal and warning against any further repetition of such behaviour. Pilate risked losing both his position and possibly his life if he refused to heed the Jews request for crucifixion. Thus the comment by the Jews 'if you let this man go you are not Caesar's friend' was a thinly veiled threat to again complain with almost certain results.

Both of the abovementioned factors would have been in Pilate's mind as he weighed up the need for justice (he possibly could have gotten in trouble for injustice as well) against the demands of the Jews backed up by their strong political leverage. In the accounts we see him vacillating and also being quite unwilling to do what they wanted, as per his normal action, but forced to by his relatively weak position.

Summary: Jesus was killed contrary to Roman justice. Pilate correctly stated 'I find no fault in him.' However the Jews exerted irresistable political pressure on Pilate whoi then gave them what they wanted.