I purchased my first brand new car in 2005, and took out a 4-year manufacturer's service and maintenance warranty.
This included the everything except tyres (my choice), and even the cost of the MoT fee. It cost me a monthly payment of £20.48.
Just before the 4 years were up, I took the car for its second MoT and, with 33,000 miles on the clock,the maufacturers instructed the service dept to fit a new timing belt before carrying out the MoT. It cost me nothing but, had I not had the cover, the decision to change the belt or not would have been down to my cost/risk.
I can only say that I considered it to be good value for money; you do have the benefit of being able to set a known budget for your motoring.
I changed my car for another new one this March. The monthly cost has increased to £27, but still worth having.
Assuming that I may not change at the end of the present 4-year period, I will decide on whether to extend the cover at that time; depending upon cost versus amount I can set aside for unknown future repairs.
Personally, I would not advise anyone one way or the other; it is a decision too intimate to personal circumstances.