For those who are internet wonks (or who ran an ISP -- like me) -- There is more to it than just TTL involved.
There is also the "min" and retry time in the SOA record. If you intend to move a domain at some time in the next several weeks you want to both bump the serial number *and* adjust all of the TTL figures to something short but rational (an hour is fine for most modest-volume e-commerce sites.)
There are also sites on the 'net running caching resolvers that *ignore* those settings, but that sort of intentional damage can't be gotten around. Fortunately those sites tend to be few in number and impact with a couple of notable exceptions in the mobile phone space.
Just remember to put the TTLs and such back when your move is complete, as dropping them does materially increase load on the DNS infrastructure.