Make a habit of looking around. It won't happen often enough if you have to consciously think about it, so actually develop the habit of looking around you. Check over your shoulder at least once per 20 steps, and keep count until it becomes muscle memory. Let it become a habit every time you're walking in a crowded area until you no longer have to keep count.
Also if you don't have a concealed weapon permit, keep a pen in your pocket at all times - a tough metal one with a sharp point. If you are alone and feel threatened, first reach into your pocket and call the emergency number and act like you're talking to a friend. Mention your location. Then with your other hand, put it in your pocket and take hold of the pen with a fist grip, point facing opposite side of your thumb.
If you have to fight, the pen can be used to stab the pectoral muscles, eyes, or groin of your attacker. This will cause extreme pain and give you a chance to escape. It will look like you're just using a fist so their arms will probably go up high, leaving the pecs open. The upper thigh is a last resort target but usually this is covered by jeans which are tough for a pen to break through. Practice by quickly going from your pocket to stabbing a target like a pizza box at eye level, then one at pectoral level, for an taller-than-average height man standing elbow-length away from you.
Just a reality check: a pen is not much of a weapon and it never will be...but in a life or death situation it's better than nothing. You can take it anywhere without a permit. If someone is going to rob you they'll stay at more than arm's length and pull a weapon, you should just comply if you can do so safely. If they get close enough for the pen that means that they're going to kidnap you or worse, so you should fight like your life depends on it (since it probably does).
Aside from general suspicious behavior, some things that should trigger alertness:
Someone approaches from behind, walking faster than normal.
Someone you don't know is staring directly at you making eye contact.
Someone is trying to distract you. Common instances include running towards you and waving, approaching you with a "sob story", or acting overly animated. It could mean they're working with someone else who is behind you.