> Is even near (but slower than) light travel possible?
Sure; send yourself as data. ;) Just don't use comcast.
On a less flippant note, in addition to the interstellar dust issue, another fun engineering problem is providing the energy necessary. If you want to send a 50 kilogram person to .99c, you'll have to provide about 4 months worth of the United States current energy production (7 quadrillion btu per month or about 7 exajoules)[1].
Now, if you are wiling to increase your flight time by a factor of ten (reducing yourself to .1 c), you can cut this down to merely 15 days worth of California's total consumption[2]. Mind you, that's just the poor 50 kilogram astronaut. The space shuttle weighed in at 75,000 kilograms (empty). So plan on using about 9 months of the United States energy production capacity for your dinky .1 c.
Given that you'll probably want to STOP once you get where you're going, antimatter engines are probably a prerequisite for relativistic space travel.
Water is really good at blocking proton radiation (those stray hydrogen atoms in the interstellar medium become really dangerous once you go fast enough). Plus you can drink it.
You also don't want to stop particle radiation too quickly, or you get x-ray Bremsstrahlung. So something a little less dense than steel works better in practice.
... yeah, and water your greenhouses (you're going to be in space a very long time), split it to generate O2 for breathing, etc. It's also probably a lot easier to find water to replenish your shield along the way, or at your destination, than steel or lead.
One thing which might be of (tangential) interest here is the novel The Songs of Distant Earth, by Arthur C. Clarke, where the replenishment of this sort of ice buffer plays a prominent role in the plot.
