I switch my car insurance every 6 months to save about $200-$250 a year. Geico and Progressive both offer big "switch now and save" discounts that disappear when you go to renew. So I take the 6 month policy to get the new policy savings, then switch to the other after the 6 months is over and the price goes up. Been doing that for about 8 years now and it keeps working.
The $64K question is how much of a hassle is it to switch? If you have to jump through a bunch of hoops to get the new policy don't bother. If it takes 2 minutes and a couple of clicks, go for it. Insurance companies are a necessary evil, but they're all rip-offs. Take the one that will rip you off the least.