Ok, when you think about posture exercises you might think about Army recruits trying to stand straight up while a drill sergeant screams in their face, "Suck that gut in. Pull those shoulders back." Well, the aikido and judo ideal of good posture begins with relaxed, mobile, and upright. While the old drill sergeant might have gotten upright, he sure missed the relaxed part.
The folks that probably know the most of anyone in the world about functional posture are the Alexander Technique folks and the Feldenkrais Method folks. I've written before on the crossover between aikido, judo, Alexander, and Feldenkrais principles, including a recent article on a neat Alexander trick for fixing neck posture. Feldenkrais has some similar exercises which involve repeatedly sitting and standing from a chair to reprogram the neck muscles. Here's something that, so far as I know, is of my own invention... Walking up and down stairs to fix neck posture.
Try this. Get a flight of steps and walk up and down sliding your hand on the rail for balance. Repeat the flight of steps several times. First this will help your leg and cardiovascular strength if you do it regularly, and having better wind means you don't have to use shoulder and neck musckes as accessory breathers. So they can relax and control your neck posture more efficiently.
Second, keep breathing as you walk the stairs. If you are not used to walking stairs you might, without thinking, hold your breath and drag yourself up by the handrail. If one flight of stairs wears you out and leaves you breathless, look to see if you're doing this.
Third, and this is the really neat part, try the Alexander trick I previously posted while walking the stairs. Concentrate on moving however you have to in order to get your nose forward and upward. As you descend the stairs, imagine your face lifting forward and up, so that your neck gets longer and straighter and more upright as your body descends. As you climb up the steps, imagine leading with your face. Imagine someone gently holding your chin and the back of your head and giving you a little lift as you ascend. Notice that getting your nose and face up and forward releases tension in your shoulders (because you can't raise your face if your levators scapulae are in contraction) and frees your breathing (because your shoulder muscles are hooked to your rib cage).