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Though saying that, we could probably travel to distant planets and explore, as time slows down the further away from gravity you are, and so you would probably not die of old age.
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Time is relative. If time slows down, you would not realise it, because if it ever slowed down, so would everything else. Including your brain. As far as you would be concerned, everything would be happening at the same speed that it normally does. A year would still go by to you, but to an unaffected observer, that year may take many years to occur. Unless you could somehow create a seperate time continuum around your brain, to allow you to witness everything going by very slowly. But this would just cause your brain to age faster than your body.
It's very much like slowing down a video replay to create a slow motion effect. The person still travels from point A to point B in the same relative timeframe and does not notice a difference, the only difference is, that time is altered so that an observer would see it as happening slower - this has an interesting factor in that a person travelling in slow motion, then coming out of slow motion, will have aged less than the observer during that period of time. Theoretical physists do not know precisely what would happen if this occured, but they are certain that it is most definately time travel. The tradeoff that prevents this time travelling from occuring to our benefit in terms of space travel, is that areas in which time is slower, take you exactly the same amount of time to travel through as they would if time passed at normal speeds.
In an area where time slows down, a ship travelling through that area would theoretically slow down also. Basically, if the distance would take 89 years to traverse at normal time speed, then it would take you the same amount of time to travel it at slow time speed - the only difference is, that it would be a very slow 89 years to someone who was observing from an area in normal time. This would mean that you would still die of old age, unless, again, you could create a seperate time continuum around the ship, but not you. The idea of creating a human stasis tube in which time passes slower than it does in the rest of the ship is one that is not new to science fiction - in fact, keeping someone young while travelling for hundreds of thousands of years has been in nearly every single science fiction novel and movie in which starships do not achieve superluminal speeds.
Now, it is theoretically possible to travel into the future by entering an area of slowed-time-space, and staying there for a while. If time travelled half as fast in this area, then staying there for a year would mean that you would be a year younger than you should be when you emerge - in other words, you would've travelled two years into the future, instead of just one. Interesting eh?
