A comment to SSCrazy reply.

Why it has to be acceptable for all applications to be down at the same time? What if we move databases slowly, one by one, to a new box?

Let's say today I am moving Citrix database at 7PM.

So I notify users that Citrix will be down for 3 hours, move database to a new SQL box, test Citrix with new connection string, done.

I don't have to restart or interrupt new SQL Server box.

So all other apps will continue to be up and running.