Sammies sometimes leave Ankh-Morpork to serve in the Watch in other cities on the Discworld, and being a Sammy is a guarantee for instant promotion anywhere. They are reputed to be efficient, brave and only moderately corrupted by bribery (only the occasional free beer, for example).
Thanks to the Sammies in other cities, the network of policemen is working closer together. By use of the Clacks towers, Sammies everywhere are communicating with each other, giving invaluable advice or news concerning criminals, and thus helping to prevent or punish crime more efficiently.
The Roundworld reference is to the first policemen that ever there were in the civilised (i.e. English-speaking) world: the Metropolitan Police founded in London by Sir Robert Peel in 1829. Met policemen are still known as "Bobbies" ("Bob" being a shortened form of "Robert" in colloquial English). Another nickname, now defunct, was "Peelers", leading to the concept that Watchmen may yet be known as "Vimers"...