Exercise is a great way to clear your mind. Physical activity stimulates your mental facilities and gives your cognitive center a direction to go. It is one of the reasons they say they are going for a walk/run to clear their heads.

But for those that can't get physical, focusing on a goal can sometimes be just as good, which is why so many replies here talk about gaming. They are focused on a task, so their brain tries to work it out/block out other stimuli. Games that are not challenging or stimulating are not as effective.

It reminds me of a person driving with the radio on, and trying hard to find the directions to a location (this is pre-voiceover GPS days) the driver usually turned the radio down or off in order to better focus. The radio in this instance, could be likened to the intrusive thoughts.

Sometimes intrusive thoughts can be a byproduct of over-saturation of neural-chemicals. One of the ways our bodies tries to get rid of it is by crying. They have found a mix* serotonin, dopamine, and norepinephrine in tear liquid. A lot of times when people are really sad, or angry, the response they feel to cry is their brain trying to force the excess chemicals out in order to get things back under control. When people resist that urge, (men don't cry, etc) they are just keeping their brain from rebooting and keep the bad mood for a lot longer than needed. It is like letting your laptop go blue-screen and waiting for the battery to run out instead of hard-resetting it.

Jwan4321, on the post above, has raised some very good points, concerning brain chemicals and intrusive thoughts.

Speaking for myself I suffered from OCD for a very long period of time, first starting in my early teenage years.
Even though it's now cured it became so bad that, in the last years, I couldn't even read, watch TV or play video games properly, because of the intrusive, obsessive thoughts. The fact that I absolutely refused to take prescription drugs (addictive in the long term) made it worse (because my mind wasn't numbed).

As with everything in life, your thought patterns can be changed with hard work and discipline. It's not easy job, but with determination you can do it.
I can only give these two small suggestions:

1 - Get a large punching bag. Physical exercise is very good. But a gym can be troublesome because of the other people, noises, etc. Running can also be beneficial, but some people don't like jogging.
With a punching bag you can channel your rage and frustration into the bag. Punch and kick as if you were beating your dark thoughts to death. You'll feel tired but relieved in the end.

2 - Discipline your mind. The same way you have to sometimes "discipline" your brain to do hard stuff (like going to school or work, when you don't really feel like it).
Whenever you're having intrusive thoughts, focus and try to guide your mind to other fields. This can prove very difficult because it can feel like you're "arm-wrestling" your own brain.

The trick is not to be brutal with yourself. Instead use the "flow like a river and bend like a bamboo" martial-arts philosophy, so to speak
When you start having a dark thought, pause, close your eyes, breathe slowly and think: "this is not my real mind - this is my brain playing tricks on me - I will think of good things and no harm will come to me". And keep thinking of different stuff, locking the dark stuff in the back of your mind. After a small time, those thoughts will vanish and you'll start thinking of different stuff.

It may seem hard at first, but it will become easier the more you do it.

You see, your physical and mental actions will gradually affect the neurological patterns of your brain. The same way you can build muscles through physical action, you can grow a "stronger" brain by having a healthy mental activity.

I'm saying all this because it worked with me. And I've seen it work with other people I know.
Unfortunately, most people can't get over their mental problems because our society loves to see miserable people (in my own country, to a certain degree, depression almost became a "fashion disease") and the pharmaceutical lobby has a great interest in keeping people addicted to anti-depressants. In fact I suspect that anti-dep meds are one of the health industry's best source of income.
In my country, people aren't encouraged to face and overcome their problem. Instead the doctors usually give them X pills and tell them to continue with their lives.

Investigate a bit further and try to see what tricks can work best for you. I also suggest you take a look into the logotherapy field.

Indeed words lead to confusion when two people meet that attach to it different meanings. They become an obstacle to understanding if one starts to confuse the symbol with the concept it was intended to represent. This certainly is true for a number of words, e.g. "god", "meditation", "awareness", "(un)conscious". For instance in the common usage of the words "conscious" and "unconscious", one would rarely describe a person giving a speech as "unconscious". Or for that matter would you call someone deeply absorbed by a thinking process "unconscious". What could be more conscious than thinking after all? But if I was to substitute "aware" with "conscious" when I wrote "become aware of your thoughts", there would be a different meaning behind the word "conscious". In this sense, there is nothing more unconscious than thinking.

Already what I just wrote will probably seem confusing. This is not because it's difficult to understand, but because what I try to describe can only be really understood through direct experience.

There are practices that involve bringing your attention to an object and bringing it back again and again, when the mind starts to wander. That is also called "mindfulness practice". Then there is what I called "dropping into the present moment". The difference between the two is that in the first case you bring your attention to one particular aspect, whereas in the second case there is no such focus at all. In the book "The Mindful Way through Depression" this difference is being referred to as "awareness vs. choiceless/pure awareness". This difference is inessential. What is important is the thing that stays the same, namely the quality of your awareness. Again this is something that can only be hinted at with words, as it has to be directly experienced. But a pretty good indicator is the peace that you feel at this particular moment. If you can't feel this deep inner peace, than this probably means you are still "resisting".

The difference between the two practices however has some practical significance. Indeed as you write
In the beginning (especially if you have been fleeing from the present moment for a long time) it will be difficult enough just to stay in the present moment, let alone being able to "drop all resistance". At least it was for me! Usually the mind is just "all over the place". A meditation practice that focuses the attention on some object, especially if it is an accessible body sensation like the breath, help to stabilize your attention. This is basically training your metaphorical muscle in the brain.

However in the end, it is not about doing formal practices, but about how you experience every moment of your life. In this sense sitting in a lotus seat with your eyes closed is no more of a practice than waiting at the bus stop.

It is also not about getting rid of all pain and negativity, but about not generating more of it yourself. Indeed
Like alcohol, food, video games or movies, meditation practice can easily become just another way to flee from the present moment.

That's ironic, isn't it supposed to make you be as present as possible with complete self-awareness? I suppose some who learn it may not get the original idea but use it as a tool, like the others you mentioned, as a form of escapism.

Even if you know the difference between these two ways of using meditation, it is still possible to slip into the habit of using it to avoid unpleasant emotions, rather than facing them. The ego is very resilient.

Realize that they're cycles, and like all cycles, they tend to find their end eventually. Bad thing is they come back around again. Kinda like a bad rash. Slap some powder on the rash and go about your day.

Life is going to suck at times for all of us. Understanding and accepting that will allow you to lift yourself up by seeing the same thing happen to others. XD

Yes! You just need to remind yourself that the rain will eventually end. There's been some points where I've gotten trapped under my negative thoughts to the point where they started affecting me (insomnia, depression, anxiety…)

I've managed to interrupt the pattern by calling friends to see how they are doing (gets me out of my head for a while), going out, anything to break the pattern--stay busy, find some easy goal and accomplish it.

But, there's also something to be said about meditation as long as you do not get mired in your thoughts again. In some ways exercise can be like this. I've found Tai Chi to be a mix of both.

The key is to become objective enough to "have your thoughts rather than your thoughts having you."

Heh thanks for this!!
I do myself have teachers who are committed to aiding me. Another thing altogether is how committed one is :)

The quality of insightful responses here is heart warming. Thank you everyone and maybe you as well have learned something, I know I have : )

Now back to waiting to go to the gym, waiting because I wiped out HARD on the treadmill and got a couple of sprains.