For any form of physical exericise or sport stretching is an important part of the training that you must do. Generally it is used as part of the warm up and is an effective way to loosen and warm the muscles and joints prior to more strenusous exercise so as to reduce the risk of injury. The increased flexibility that you gain from stretching will also increase your range of movement, therefore improving your agility and further reducing the chances of picking up an injury through over exertion.

In martial arts, whatever tradition or style you happen to follow, the importance of stretching and developing an improved level of flexibility is even greater. There are two main reasons why it is so important - because many techniques such as high kicks cannot be performed at all unless you have the requisite level of flexibility, and because a great deal of stress can be put on the tendons and ligaments of your joints during martial arts training and most particularly during an actual fight, and a good program of stretching will serve to increase the strength of your tendons and ligaments as well as increasing your flexibility.

Although I do not have the space on this single page to run through a complete training regime I will assume that anyone reading this will be a student of martial arts and will therefore have already learned a few stretching exercises as part of the training at their club or dojo, so I will focus here on some general principles to help you gain the most you possibly can from your stretching. If you want to really step up to the next level with your flexibility then you may also want to take a look at this other hub I wrote on the use of stretching machines

1. When doing your stretching as part of an all round training session you should consider dividing it into two sets, one to be performed at the beginning of the session as part of your warm up and one later on in the session, perhaps right at the end. Often stretching is used purely as part of the warm up, but like any other physical training if you want to get the most benefit from your flexibility exercises then you should already be warmed up before you do them. Dividing it into two means you can still get the benefits of using these exercises as part of your warm up routine, but you will also be able to push yourself further and make greeater gains whilst performing them later on in your training session.
2. A short 5 minute stretching routine first thing in the morning can make a big difference. Personally I can notice a significant improvement in my flexibility throughout the whole day when I do this, and can push myself harder and further without pain when I do similar exercises later on in the day.
3. Don't forget to loosen up your joints as well as the muscles. Spending 2-3 minutes doing this before you go on to do your stretching helps you to push yourself further without pain and the risk of injury. Circling the hips, putting your hands on your knees and moving them in circles and swinging the arms around are all examples of quick and easy exercises to help loosen up the joint.
4. Introduce as much variety as you possibly can into your routine. Don't just stick with one, or even two exercises for each muscle group. This doesn't mean that you have to do a massive number of exercises every time you train - you can use one per muscle group in an individual session, as long as you do something different in your next session, and then something different again the time after that. This is important because no single exercise can replicate the wide range of movements, each with a different stress pattern, that you would experience during a fight. The more variety you put in the better you will be prepared to deal with any situation effectively and without the risk of injuring yourself.
5. Don't forget your upper body! Many programs will focus on the lower body because it is this area which requires greater flexibility for specific techniques, but you should remember that your training is also to prevent injuries and must also include your chest, shoulders,  arms and neck.

Yoga can be a great way to help you develop not only flexibility but also balance and stability. Going to a general Yoga class can be a big help, but you might also want to look at some of the yoga programs developed specifically with martial arts in mind. Take a lok at this article on Martial Arts Yoga on the TheYogaHub.net website.