But they can be far from entertaining when they end in collisions or injuries to drivers or passengers.
One UK police force has become so concerned about its officers and vehicles taking part in pursuits or chases that it has decided to ban them.
Humberside police says this is not a brand new policy and has been in place for a while, but the force went public in The Daily Mail newspaper and confirmed that all pursuits will be stopped.
Breakfast heard from Assistant Chief Constable Alan Leaver from Humberside Police. His force makes use of a helicopter that can spend up to 20 hours in the air, and also employs the stinger device to puncture cars' tyres and end prevent the need for a pursuit.
 | Deaths & Serious Injuries from Police Accidents 2001/2002..... 24..... 168 2000/2001..... 19..... 163 1999/2000..... 14..... 115 1998/1999..... 11..... 210 1997/1998..... 15..... 200 |
But critics say the policy is becoming "a charter for car thieves" - the police want the chases stopped even if it means the car thief doesn't get caught.
ACC Leaver says the helicopter is very effective and hard to shake off; it usually leads to cars being abandoned.
Recent figures from the Home Office show deaths during police emergency calls have risen over the past few years.
In 2001/2002 there were 24 deaths in England and Wales because of police emergency calls - in 1998/1999 it was only 11.
During the same two periods there were 168, and 210 serious injuries for the above two periods.
Concerns
The RAC Foundation which sets policy on motoring issues said the move by Humberside was "radical and brave".
It remains concerned that whatever kind of car you're driving, you're in the hands of the laws of physics.
Driving is fast and dangerous, and as speeds increase so do breaking distances - dramatically.
That's one of the things which concerns the RAC, who say their main concern is for the other road users and their safety.
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