Potentially any time you book a ticket that involves flights from multiple airlines. In such cases the ticketing airline (say, DL) will usually "want" to book the other airline's flights using its own DLxxx codeshare, but (1) sometimes it doesn't have a codeshare on that particular flight (examples for DL include some flights operated by AS or HA, but also some less commonly traveled foreign partner routes), or (2) specifically for DL, if you use an upgrade certificate to upgrade an AF/KL partner flight the mechanics of the process will require DL to convert the flight to an AF/KL marketed number even if you originally booked it as a DL codeshare (3) there are also manual ways to ask for, or use ITA Matrix to book on your own, a mixed airline itinerary with different marketing carriers.

As flyerCO alluded to, some airlines refuse to issue tickets that don't have at least one segment marketed by themselves, but others don't (I once had an all-DL itinerary that I couldn't get to price out on DL's website but managed to get it ticket by Air Canada lol -- I ended up cancelling it within the 24-hour risk free period though)