Even if you could go 1% the speed of light that is still 1,860 miles per second or 6,696,000 miles per hour. If you could bleed 25 miles per hour off of that every second it would take 3 days to come to a complete stop. If you have ever had to slam on the brakes you know that quick of a stop does not feel to good.
To add, at that speed a 1 gram object would have the energy of 100 tons of TNT, or 10 tens the energy of a Airbus 380 at cruising speed. So a space craft that strikes a pebble going 0.01c is going to have a very bad day.
Technically, a spacecraft can only use half its fuel-vs-momentum to accelerate, and the other half to decelerate, unless an aerobraking maneuver is available. At a significant percentage of the speed of light, however, this is impossible. Even 1% speed would fry you faster than a moth in a flame. I personally think our own solar system holds enough room for us to explore for the next million years if we survive that long.