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Scientists proved that Earth's magnetic field accumulates antimatter produces in collision of cosmic rays with matter, in certain zones near the Earth. In these zones antimatter is 1000 times more concentrated than usual. The amount of antimatter that could be collected in one year is enough to make an interplanetary trip to Saturn, which magnetic field collects  even more antimatter. Speeds would be tremendous, with constant acceleration of 100km per seconds, which means that spacecraft with this acceleration would soon reach the speeds close to the speed of light. Traveling to planets in Solar System would take hours or days to complete. Near the Saturn, there is enough antimatter to travel to stars.
Now it's all the question of money, and a few technical problems.

http://www.bbc.co.uk/news/science-environment-14405122

I wonder if that'll bum out CERN with their new anti-proton factory, the antiproton decelerator.

Still, at speeds less than light we won't go very far very fast... and aren't they already creating anti-matter in abundance in various cylotrons around the world?

I remember being shocked that they are already using anti-matter in medicine in the PET scan

That made me LOL, the few small technical problems could take hundreds of years to overcome.  In theory, lots of the science in Star Trek is possible but the practical application of these things is beyond us.  Would be interesting to jump 500 years and see if we have made much progress but I have a few technical problems with my time machine

Oh really? Could you at least vaguely discribe to me the technology the allows us to contain and store any significant amount of anti matter? Just so you know, even handling pure hidrogen is a big problem...

what happens if your traveling at near the speed of light and you hit a speck of space dust  or a fragment of an asteroid etc. I'd like them to work that out before I buy a ticket.

Just a simple magnetic field is able to keep antimatter in a container. The electric power needed to produce and maintain such a magnetic field is completely achievable. I mean, it's possible today, and it's even not so expensive. Antimatter particles are electrically charged, and they act like any other "matter" particles.

Not the same, as speed increase, the amount of damage that a small particle can do magnifies.  It would be like flying through bullets with only paper to protect you.  Then there's the radiation, that will also kill people travelling vast distances through space, unless they use heavy shields and that makes it harder to go fast.

Not in the 2.4 GHz unlicensed band, please: I am already struggling to find a free channel for my wifi

You can store sunlight in lots of different ways - plants turn it into oil and coal, for example, gases produce winds because of it. My solar panel creates hot water.

Wow, you are telling me to read more science books. That's the only thing I read. Of course I know it would be a big boom if antimatter escapes from the container. But basically, if you keep the power on, it can't escape. You sound like those people who couldn't believe that nuclear power can't be controlled. Of course we all know that any nuclear plant will make a disaster if we stop to cool down the reactor, but we still have nuclear plants. Also, the amount of antimatter that can be collected around earth is measured in nanograms, and it doesn't have to be brought down to earth. Nanograms are not enough to make a disaster on Earth if the ship is far enough.