I also noticed I had a pretty bad posture problem about 8-9 months ago. Since then, it has greatly improved. I like using this test to make sure my posture stays proper:
Stand with your back to a wall. Your heels, butt, shoulder blades, and head should touch the wall.
You want to keep your head back with chin down like you have a double chin, your shoulder blades down and back, and push your rib cage up and out. It takes some practice, but it's not too hard to improve if you are conscience of it. Basically, you want to try to maintain the two natural curves at your back, from the base of your head to your shoulders, and then your your upper back to the base of your spine.
Also, if you don't want to sit all day, you should try a standing desk. Basically, its your desk only at the height at which you can work on while standing up. Some desks can be modified so you can sit down and still work while you take a break from standing. I tried a standing desk over the summer and it helped a ton! So now I use one all the time (I can sit or stand at it). It has a ton of benefits including better posture, burning more calories, and some say they feel more productive while they are standing up. If you want to get really fancy, instead of standing you can walk on a treadmill while on the computer. I know a guy who's done that and a pace of about 1-2 miles an hour you can walk for hours.
Another thing you can try is to put things that you need while at the computer like kleenex or your phone in a location where you have to stand up and walk over to get those items. That way it forces you to stand up every so often.
I found that lat pull-downs helped a lot with my posture too as long as you have good posture when you do them.