A sometimes overlooked muscle is the iliopsoas, more commonly referred to as the psaos.
If you sit a lot (or fight MMA from guard a lot), your iliopsoas can shorten or tighten and pull on your spine.
As you can see from their EXRX entry, the iliopsoas are responsible for hip flexion (think, pulling your knees to your chest) but also attach to the spine. Thus, if they get tight, inflexible, or short, they can pull on your spine and give you back pain.
Iliopsoas on EXRX
It's discussed in even more detail at this link at EXRX:
Hip Flexor Inflexibility
Here are some ways you can address this issue.
This article on stronglifts is a good primer on referred pain - tight psoas leading to back pain.
The Psoas - Is It Killing Your Back?
Next, a large portion of the exercises on the Egoscue Basic DVD are aimed at getting the hip muscles in balance, and can go a long way towards releasing tight hip flexors.
Joe DeFranco made one of my favorite videos on releasing the psoas. You'll need a theracane or something similar. Joe has back issues (congenital, not exercise-related) and knows a lot about relieving back pain. I can personally vouch for this one being a) painful and b) effective.
Joe DeFranco Psoas Release
Kelley Starrett also has a video which also discusses the hip in general as well as the psoas.
Episode 25: Hips
Finally, there are a lot of useful stretches for the psoas and the surrounding muscle tissue which might be causing the psoas to tighten up in the first place. This article on "Yoga for Fighters" shows many of them.
Yoga for Fighters: Releasing the Psoas
Finally, if your psoas are very tight and you want expert help, consider A.R.T. - a practitioner can easily (albeit painfully) release your psoas. I personally go to Fine Tune Therapy when I need A.R.T., but there are qualified experts all across the country.
If you get back pain from sitting or doing standing exercises, it's worth investigating if the problem isn't the lower back but the front of the hips.