Generation Ships: The Empire itself has never used generation ships, despite thinking of the concept. Regular lighthuggers don’t count – the whole immortality thing means that while children may well be born en voyage, the people who got on will by and large be the same people who’ll get off. Their first burst of interstellar colonization (the Thirteen Colonies) was done subluminally, but the Deep Stars carried frozen colonists, so they don’t count either. And the wandering city-ships don’t count simply because they’re not a means of transport, they’re places people live – and people come and go all the time, any time they pass through a system.
Which is not, of course, to say that the concept’s never been used by anyone else; I’m sure it has, probably quite a bit, and still is in places beyond the Associated Worlds, or where they’re still en route. And, arguably, the couple of nomadic cultures (the londian, for one example) who live on wandering city-ships and have nowhere to leave them for but other city-ships might well count.