Grimspace by Ann Aguirre

Sirantha Jax is part of a vanishingly small subset of people-- those who are genetically able to navigate "grimspace," the interdimensional subspace where ships can jump between distant parts of the galaxy. Unfortunately, the last ship she piloted was in a horrific, fatal crash. Many important people died, including her boyfriend/co-pilot, and she was ruled responsible. After months spent languishing, guilt-ridden in a cell, she is rescued by a tall, handsome stranger who wants her to navigate his ship and its motley crew on their secretive, rebellious mission. Jax decides that things can hardly get any worse, so off they go. They adventure across various planets, interact with alien races, get brainwashed, end a blood feud, accidentally adopt a baby frog-creature, uncover a government conspiracy, and generally have a wild ride across the galaxy.

While fans of old-school sci-fi (Asimov, Heinlein) may roll their eyes at this one, Grimspace is a funny, action-packed romp that would have a lot of appeal to fans of the Wayfarers series, shows like Firefly or Torchwood, or even the urban fantasy genre. Jax is snarky and hilarious, and the crew makes for a great ensemble cast. It's weird and unpredictable in all the best ways, and is well worth the read if you like your sci-fi a little wild.