Assuming we had technology that could accelerate a space craft at 1G indefinitely, the result for the occupants would be normal gravity. (1G of acceleration would feel the same as earth's gravity)
Effectively acceleration is artificial gravity.
If that space craft accelerated at 1G half way to Proxima Centauri (2.1 lightyears) and then decelerated the final half at 1G, (2.1 lightyears), the trip would take 4 years and the occupants would experience normal earth gravity for most of the trip:
Acceleration: 9.8m/s/s
Distance: 19867533992419680m = 2.1 lightyears (to half way mark x 2 for the entire trip)
Time: 63675731.43642089s = 2 years (to half way mark x 2 for entire trip)
Freefall time/distance/speed Calculator - CalcResult
Speed at the halfway mark: 624,022,168 m/S which is impossible since that would be twice the speed of light (299,792,458 m/S).
I'm not a physicist or an expert in this area, but I believe this means that the time of 4 years would be the time experienced by the spaceships occupants, not the time experienced by the stationary observers on earth. Observers on earth would perceive a longer voyage time because of relativity's time dilation effect. But its the experience of the occupants of the space ship not the stationary observers that counts which would be 4 years. I am unsure of how long this trip would take from the stationary observer's viewpoint, taking into account relativity's time dilation effect.
So yes I believe its feasible to travel to other stars and habitable planets within a lifetime, given a spaceship which can accelerate at 1G indefinitely. We just don't have this technology yet....
FYI:
The time to Gliese 581g (the nearest known Habitable Zone planet is 22 light years away) would be 9.2 years using the same technology. ( the further the distance, the longer the period of acceleration, the greater the peak speed, the greater the time dilation effect....)
wiki:
Interstellar traveling speeds
If a space ship is using constant acceleration over interstellar distances, it will approach the speed of light for the middle part of its journey when viewed from the planetary frame of reference. This means that the interesting effects of relativity will become important. The most important effect is that time will appear to pass at different rates in the ship frame and the planetary frame, and this means that the ship's speed and journey time will appear different in the two frames.
Planetary reference frame
From the planetary frame of reference, the ship's speed will appear to be limited by the speed of light—it can approach the speed of light, but never reach it. If a ship is using 0.5g constant acceleration or greater, it will appear to get near the speed of light in about a year, and have traveled about half a light year in distance. For the middle of the journey the ship's speed will be roughly the speed of light, and it will slow down again to zero over a year at the end of the journey.
As a rule of thumb, a constant acceleration ship journey time will be the distance in light years to the destination, plus one year. This rule of thumb will give answers that are shorter than the correct answer, but reasonably accurate no matter what the G force is as long as it is above, say, a half G.
Ship reference frame
From the frame of reference of those on the ship the acceleration will not change as the journey goes on. Instead the planetary reference frame will look more and more relativistic. This means that for voyagers on the ship the journey will appear to be much shorter than what planetary observers see. This is important. It means that a journey that appears to take decades or centuries to planetary observers will take years or decades to the journeyers. This difference makes space commerce feasible for the ship crew even though it looks unfeasible for those on the planet they leave behind. A journey from the sun to the galactic core at 1G constant acceleration takes 340 years as experienced by the ship crew and 30,000 years as experienced by Earth observers.[1]
This is something many readers don't understand well, so it bears repeating: The journey times as experienced by those on the ship are not limited by the speed of light. Instead what they experience is the planetary reference frame getting relativistic.
In the ship frame of reference the amount of acceleration applied will change the journey time: Larger accelerations will produce faster journeys. That same journey to the galactic core will take 244 years at 2G and just 110 years at 10G.[1]
http://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration#Interstellar_traveling_speeds
