Power Girl originally had powers similar to those of the original Superman: super-strength, flight, invulnerability, X-ray vision, heat vision, and super-hearing. However, after sustaining severe injuries early in her JLE days, she was left significantly weaker, could not fly and lost all of her vision powers and enhanced senses. She eventually recovered her ability to fly and remains a powerhouse nonetheless.
In 2005 issues of JSA, she has also been shown using her super-hearing to listen through walls, heat vision against Black Adam in Kandhaq, the latter temporarily blinding her.
Her powers appear to be exactly the same as Kal-L's as of Infinite Crisis #6. She also has an occasional weakness to kryptonite, which may well be explained by her newly (re)established Earth-Two origins. In pre-Crisis times, kryptonite from one dimension did not work on a Kryptonian from another dimension; this limited immunity may therefore be a result of the merging of dimensions during the Crisis. As of Infinite Crisis #7, it has been positively shown that the Kryptonite available in the mainstream DCU doesn't affect Kryptonians from other universes, such as Power Girl, Kal-L, or Superboy-Prime.