One of my reader's suggested I check out his website: www.lower-back-pain-toolkit.com. It turns out to have lots of interesting information, and has inspired me to put up a post about 'good' posture.
First, what is good sitting posture? The general/traditional view is that you want to sit upright, with a gentle s-curve in your lower spine from a lumbar role. See this link for a much more detailed discussion. Whenever this 'good' posture is illustrated, the person is almost always sitting with a 90 deg. angle between their legs and their torso. Undoubtedly, this is better than the forward slouch, where your back slowly curves forward and your chin ends up nearer your kneecaps than your hips.
This traditional view, however, may not be quite right, at least with respect to the 90 deg. angle between your hips and your back. MRI scans have revealed that when you sit in this posture, you actually put a lot of strain on the disks in your lower back. It may be significantly better to lean backward at a greater angle, such as 135 deg. See this BBC article for an example of this posture, and a short discussion of the science behind it.
In my personal experience, less than 90 deg. can quickly lead to pain. Exactly 90 deg. feels much better, at least in the short term. Greater than 90 deg. seems, however, to be the least painful of all. It can be hard to get a > 90 deg. position in a regular upright chair, however, without also leaving your back unsupported and hanging, leading to a reduction of lumbar lordosis. One way to avoid this is to role up a towel and sit on it. This will increase the angle between your hips and your back, while still maintaining the good lordosis. Another option is to slouch backwards, and then support your lower back by placing both of your arms behind your back.