According to Jon Kabat-Zinn, the creator of the Mindfulness Based Stress reduction technique, mindfulness means paying attention on purpose to the present moment in a non judgmental (such that your life depends upon it). Jon Kabat-Zinn has been one of the biggest proponents of mindfulness and its use in daily and professional lives. In fact we have seen many 'spiritual gurus' gain mainstream recognition who live and preach mindfulness including such well known monks as Thict Naht Hanh.
However, long before mindfulness became mainstream in the West, it was being used, and preached extensively in eastern cultures. Buddhism is one such belief that is heavily associated with mindfulness, but many other religious traditions such as Hinduism, as well as cultural traditions, such as Tai chi and Yoga are associated with mindfulness.
However as a Muslim, during my inquiries into mindfulness, I noticed some very peculiar similarities. This however is my own interpretation but I strongly believe that mindfulness truly has a big role to play is Islamic life.
Good vs Evil:

Let me start of with the basics. In Islam a struggle has been depicted between one's self and the Satan's whispers. Satan has vowed to try his best to ensure a devout muslim goes of the righteous path, while a muslim must exercise sufficient self control. In such a manner, I believe the very struggle for salvation in islam is related to self control.
In the islamic belief anyone studying the Quran or performing the obligatory prayers, is bombarded by the Satan. We are expected to bring our attention back to our task. Therefore to me the whole idea here seems to be to control the self against the devil (the wandering mind) and eventually exercise better self control.
Start With the name:
In Islam we are expected to start everything with the name of Allah. Whether it is prayer, or reading the Quran , we are expected to begin by Allah's name and do it with full concentration. When one takes the name of Allah, it ensure we are mindful and aware of what we are doing and why we are doing it. This in itself is similar to the STOP acronym used in Mindfulness or Breathing before starting something.
the idea of starting with the name of Allah goes beyond religious practice in Islam and ensures the task is completed successfully
Meditation:
Mindulness meditation talks about formal meditations, that are practiced everyday often several times a day. Reading the Quran eg I believe is a form of meditation. Apart from that Muslims are expected to pray at least 5 times a day, with full concentration. Not only are these like mini meditations, they are in fact like yoga, as they require the Muslim to switch between different poses. When can lengthen the prayer as the day passes, almost ensuring that the person is completely 'switched off' before bed.
Awareness and Remembrance:
Muslims are encouraged to remember Allah at all times. This is often done through such things as saying 'Start with the name of Allah' before commencing a task or or 'All praise be to Allah' when something positive happens or 'God Willing' when we wish for something to happen. At all times, we are to remain aware of God and the role he plays in our life. The tradition of Dhikr or remembrance of God, is also about ensuring that one keeps God in their mind all the times such as in gathering.
Also, Islam traditions have laws and prayers regarding such things as what to say when entering a mosque or going on a travel or better methods to undertake such mundane daily tasks as how to eat or even take a bath. Although these might be considered optional, it goes on to show how mindful a Muslim is of his or her actions. In order to do it right, they live in the moment.
Conclusion:
As I have mentioned above, I see many similarities between the concepts of mindfulness and believe that a practicing Muslim is someone who has regularly exercised their mindful muscle and in the process mastered self control.Other concepts, such as kindness to others, staying positive and most of all, gratitude are important concepts within Islam as well.
Although my view is simplistic, I would love to hear what you have to say about this as well.