So you don't have to remember to Annex it
You've just conquered a city you KNOW you're going to want to annex soon. (In my most recent game, I needed to force building a harbor to start up trade routes to my latest expansion, "Old Greece") Unfortunately, you're human, and simply might forget to do it later. So, rather than remembering to interrupt your 10th turn from now, you annex the city and set it to building the courthouse. Done. Nothing to remember, no turn interruption, the game will alert you when the city is ready for its next order.
This can be especially important if your turns otherwise consist only of dealing with the next item in the queue, then clicking next action/turn. I don't normally recommend playing this way just off the next action button; You will catch a lot of mistakes by stopping at the end of each turn and asking "is anything wrong? is there anything else I should do? what's the worst problem facing my empire right now?" However, the event-queue style of play can be a very fun way to play a relaxed game (far easier to get into "the zone"), or to play a game on an easier difficulty just to try something.
Everyone else has already covered the few times when it might be ideal for your gameplay to annex the city immediately, but those are sadly exceptions. So, if you want to play your BEST, you'll have to puppet the city and somehow remember to check back later to annex it. I recommend keeping notes as you play of things you need to do in the future, write down what turn you're on and what turn you want to check back, and check your list before the end of each turn when you ask yourself the questions I mentioned above.