I have to concur with all the above. My boiler, Worcester Bosch, was on a service contract from new, 15 years ago. This included an annual service plus call-outs for any repairs. It was trouble free for about 12 years, then required a simple control knob which got accidentally knocked off...engineer came, fitted it, plus new pcb, at no charge, but without the service contract he told me it was ÂŁ80 call-out charge and the same again for the parts.
A couple of years later during the annual service, the engineer replaced several components that were known upgrades to fix minor glitches (not that my boiler had suffered from these) and the next year when I called them out due to some damp staining round the boiler he fitted a completely new heat exchanger and assorted kit, all included within the annual fee. I guess I was looking at buying a new boiler at that point, but effectively I actually got one with these repairs.
Thus, imho, annual service is absolutely essential for safety and peace of mind, and if you can afford the all-in care option, go for it. Contract customers get priority in emergencies too, I believe. One tiny final point, on a contract scheme you get a bit of a "window" to have your annual service, so it can be useful to move the dates around so you get your service in July/August/September, depending on how busy they are. This means you get to choose an appointment and have your boiler serviced before winter comes, when appointments are harder to schedule.