Tru Calling, on FOX
Fox Connect; IMDb; TV.com; TV Tango; TV Tropes; TWoP; Wikia; Wikipedia
Okay. When Tru Davies was 12, her mom died. Flash forward 10 years, and she's just graduated from college, and takes a job at a morgue to prepare for medical school. (She's played by Eliza Dushku.) Tru starts hearing voices; dead people at the morgue ask for help, and then she'll have to relive the day and try to prevent them from dying. She also wants to help her brother Harrison and sister Meredith with their own problems. Harrison was the first person she told about her ability, though he didn't really believe her at first. The second person she told, who actually brought it up himself, was Davis (Zach Galifianakis), a guy she works with at the morgue, and now he does whatever he can to help her save people on her do-over days.
Tru's best friend is Lindsay. And there's a guy named Luc whom Tru kept trying to get to know, except every time she did, the day would end up starting over. Eventually they did get together, though. Later they broke up because Tru had this secret she was keeping from him. Eventually this guy named Jack Harper (Jason Priestley) started working at the morgue, who would in the first season finale turn out to also relive days, but he thinks Tru shouldn't be tampering with fate. So he tries to stop her from saving the lives of people who were "supposed" to die. It's an interesting situation, which reminds me of the "Evil Leaper," from Quantum Leap. Oh, I should also mention that at one point, Tru learned her mother used to do what she does. And the season finale has a surprise involving her father, too. I dunno what else to tell you, but I enjoyed the show. Unfortunately, the second season was shorter than it should have been, and the series didn't get a third season. So there are various things that were left unresolved.