Sticking close to your clothes in a shared laundry room is just good common sense, but it's also common courtesy. When you start a load of laundry and wander off to tend to some chores around your apartment or make a quick trip to the grocery store, you're not just risking your property; you're also risking inconveniencing a neighbor.
You wouldn't want to have to sit and wait for someone else to transfer clothing from the washer to the dryer or retrieve dry clothes that had been sitting in the machine for half an hour, so don't put someone else in that position.
Make sure to start laundry when you have time to be attentive and keep it moving. And, keep common areas clean. Wipe up any spilled detergent or other mess, and keep your supplies neatly gathered so that you and your neighbors don't get in one another's way. That way, everyone can benefit from the convenience of having facilities onsite.