There is no secret movement or stretch that is going to improve your mobility. Improvement comes from consistent action - getting into good positions throughout the day, every day! Working on movement and mobility while at the gym for 30-60 minutes per day a few times a week won't undue the sedentary or static lifestyle many of us have in the other 23 hours each day.
There are four different positions that I highly encourage you to get into on a daily basis and finding ways to incorporate them into your day.
1) Arms overhead - just get your arms up overhead. Stand in a door frame and put your hands up and stretch and move. Do this for 1-2 minutes at a time to open up your chest and lats.
2) Deep squat - this one may take a little bit of time to get into. A lot of us have mobility limitations which will cause us to point our feet out or our heels will pop off the ground. Hold onto something sturdy and sit back into a squat. Feet should be about shoulder width apart, maybe a little wider, feet point forward. The goal is to get your butt down close to your ankles.
3) Half-kneeling - kneeling on one knee with your opposite foot in front of you. Do this on both sides.
4) Tall kneeling - kneeling on both knees. Put a towel or pillow under your knees if you need to.
All of these movements can be done at your desk and at home. These four movements are key to improving your hips, lower back and shoulders. Sitting destroys our hips and causes a lack of mobility. Stuart McGill, a low back pain researcher, says when the hips stop moving, the back starts moving. The spine is meant to maintain a rigid shape while loaded all the way through movement. McGill has shown the best way to hurt your back is to move into flexion when its loaded.
I hear "I need to start doing yoga" on a weekly basis. Yoga is very beneficial, but again, it won't undue the hours of poor positioning you are putting your body through on a daily basis. Find ways to get into better positions throughout your day to improve your hip mobility and stability. Start now with the 4 positions mentioned above.