Rolling takeoffs are recommended in my company on 737s (classic and NG).
The relevant text from the FCOM:
A rolling takeoff procedure is recommended for setting takeoff thrust. It expedites takeoff and reduces risk of foreign object damage or engine surge/stall due to a tailwind or crosswind.
Rolling takeoffs are accomplished in two ways:
• If cleared for takeoff prior to or while entering the runway, maintain normal taxi speed. When the airplane is aligned with the runway centerline ensure the nose wheel steering wheel is released and the LHS applies takeoff thrust by advancing the thrust levers to just above idle (40%N1). Allow the engines to stabilize momentarily then promptly advance the thrust levers to takeoff thrust (autothrottle TO/GA). There is no need to stop the airplane prior to adding thrust.
• If holding in position on the runway, ensure the nose wheel steering wheel is released, release brakes and then apply takeoff thrust as described above.
Note: Brakes are not normally held with thrust above idle unless a static run-up is required in icing conditions.