The first thing to get straight is that stretching in the warm-up is not the same (and doesn't replace) warm-up sets. Warm-up sets are important and should be done after your stretching.
The benefits of stretching include helping to minimize injury and also helping to reduce internal friction in muscles and joints. Stretching also improves coordination between muscle groups that could help you with your techniques on certain exercises.
Stretching could also actually enhance muscle growth as stretching muscles stimulates muscle fibers. So, in a way, you are not only risking possible injury by not stretching, but you could also sacrifice some of your growth, too.
Stretching can actually lengthen your muscle and cause muscle separation to make you look more cut, as you will have more room to grow. Throughout your workout, you should keep the full range of motion to maximize your workouts. Stretching also increases the range of motion to improve your workouts.
Remember: you are at risk of injury if you stretch when your muscles are cold. This is the reason people do a few light sets before stretching.
It is very important to warm up by stretching before your routine and also at the end to cool down. Stretching minimizes potential injury by warming up the muscles at the beginning. I read somewhere that our muscles are like giant elastic bands and when you put an elastic band in a freezer when you take it out the next day it can easily snap.
There is a possibility that your muscles might be affected in the same way, by not stretching at the beginning and also throughout your program. Stretching helps prevent soreness that regularly occurs after a hard session.
The risk of developing lower back pain that can greatly be reduced by proper stretching throughout your workout. Between sets, stretch your muscles to keep blood flowing through your body.
If you stop working out for around 5 minutes (I see this often when someone stops to either give or ask for advice to another member in the gym), you should do your stretching again and perhaps a few warm up sets as you need to get your blood flowing again.
Three Types Of Stretches
There are three different types of stretching which you should try to include at the beginning (which is the most important) but also at the end (and occasionally between exercises) to keep your blood flowing through your body. These include:
Range Of Motion
Range of motion stretching (ROM) is when you move the large muscles rhythmically in gentle, repetitive motions within their normal range of motion. This is the type of stretching you should start off with to start warming up and relax the tightened muscles.
Proprioceptive Neuromuscular Faciltation
Proprioceptive neuromuscular faciltation (PNF) is a stretching exercise specifically for flexibility purposes.
Passive stretching is also good to maintain flexibility. This is performed by moving the muscles and joints slowly into a fully-stretched position and hold for ten seconds. This type of stretching should be done throughout your routine.
These are the three main types of stretching and should all be included in your workouts.
Stretching should be done for 3-5 seconds then released. You should do the same stretch again but this time hold it for around 20 seconds and squeeze a little harder.
If you are not sure of certain stretches, your gym will probably have a wall chart showing the different exercises - or ask a few experienced people in your gym (if they actually stretch before going straight into heavy lifting).
The Bottom Line
The bottom line is to get the most out of your workouts, stretch!
Saying that, do not overdo it with the stretching, as you still want to keep your energy levels up for your main workout.