If it's more than 15 years old we are told to recommend a new boiler for efficiency reasons (and if it's an open flued appliance that you have, they're only about 60% efficient at best). Either that or it's on the reduced parts list and if something breaks that we can't get hold of any more then you're stuffed. If it's not dangerous, then you are probably best just keeping it and hoping it doesn't break down on you, but the savings you can make on the gas bill will effectively make a new boiler pay for itself; so it's definitely worth considering.
Do NOT buy a cheap boiler, it will only cost you more in the long run and cause lots of hassle. Buy either a Worcester (Bosch) or a Vailiant boiler and you should be sorted for a long while. Glowworm and Baxi/Potterton are "okay" and almost every other make isn't even worth looking at. The amount of times I go to cheap makes like "ariston", "ravenheat" and "miele" boilers is staggering. There are people on contract with things like 12 call outs in a year for example. The better makes may cost £100-200 more than the cheap ones, but it's definitely money well spent.
Edit: and to clarify, you do NOT have to have a combi boiler, you have to have a condensing boiler (except in very special circumstances). To be completely correct, you have to have an appliance with a SEDBUK rating of "A" (90%+) or "B" (86-90%), but the only boilers that can meet this currently are condensing (almost all "A" rated).
