Actually, the best time to purchase an extended warranty or mechanical breakdown insurance is when the vehicle is brand new. The reason for this is an insurance concept called "adverse selection" and it effects how these products are priced. A brand new vehicle is considered a good risk since the owner has no history with the vehicle yet, good or bad. When you go to purchase coverage on a three year old vehicle, the prices will be higher because more of the owners with problem vehicles will buy coverage at that point then those that have had no problems, driving up the price. You also get to enjoy some of the added benefits longer like the travel cost reimbursements that will usually still apply during the OEM warranty period.
A few things to remember when buying an extended warranty- be sure that the dealer is selling a reputable product backed by an A rated insurer. You can negotiate the retail price (unless you live in Florida where the rates are fixed by law). And avoid the internet only providers who may or may not be there when you have a claim and stick to someone with a "bricks and mortar" presence.