There's often value in staying with an insurer for a long time, but, frankly, some get complacent and feel they have a customer for life. In those instances (and probably what Harry experienced), the insurer lets rates creep up to the point competitors offer better rates in order to attract new customers.
It's a little like the promos you see for cell phones or cable/satellite TV where they promise dirt-cheap rates for 6months or a year, but you're required to enter a 2 or 3 year contract. After the attractive "new customer only" rate ends, the regular rate is much higher and offsets the savings. You just have to be careful to compare apples to apples.
And, as Tom said, check out their claims service records and complaints ratio with your state insurance commissioner or regulatory agency. Some companies are great at collecting a lot of low premiums but not-so-great at taking care of customers.
Having said all that, you guys are right ~ it pays to shop around to make sure you're getting as good a deal as you can.
And, yes, those discounts for insuring multiple vehicles and/or homeowners/renters coverage with the same insurance company can be HUGE.