Tau Zero by Poul Anderson

The epic voyage of the spacecraft Leonora Christine will take her and her fifty-strong crew to a planet some thirty light-years distant. But, because the ship will accelerate to close to the speed of light, for those on board subjective time will slow and the journey will be of only a few years' duration.

Then a buffeting by an interstellar dustcloud changes everything. The ship's deceleration system is damaged irreperably and soon she is gaining velocity. When she attains light-speed, tau zero itself, the disparity between ship-time and external time becomes almost impossibly great. Eons and galaxies hurtle by, and the crew of the Leonora Christine speeds into the unknown.