Generating Random Numbers in SQL Server Without Collisions

From time to time, I see a requirement to generate random identifiers for things like users or orders. People want to use random numbers so that the "next" identifier is not guessable, or to prevent insight into how many new users or orders are being generated in a given time frame, but they don't want to run into any duplicates. We can trade a bit of disk space and relatively predictable (but not optimal) performance for the guarantee of no collisions, no matter how many random numbers we've already used.