Incoming links: Star system
Distance of stars nearest to the Sun as function of time
. Source. 
Some notable ones:
- Proxima Centauri, the nearest one, at 4 ly. It is part of the Alpha Centauri star system, which contains two other stars at very similar distances as well, and their relative distances to earth will change positions in a few tens of thousands of years.
- Sirius, the brightest star in the sky at 9 ly