Everyone likes their own stuff, but here's what I listen to myself:
Indie 103 - The morning show, Feel My Heat Monday nights, and Jonsey's Jukebox at lunch or at 6pm. The rest of the time it's mostly automated, or features this tedious guy who yells named "TK." Jonsey's Jukebox is probably the coolest radio show in the country. Jonsey is Steve Jones, the ex-Sex Pistol, and he plays a huge variety of his own choices: pure freeform in a major market. Mind blowing it's lasted this long!
KUSC - I'm a big classical fan, and this is the only station in town now.
KRTH - They keep popping in some new 70's nuggets, and I like the upbeat feel, especially while driving. Often have to switch away, though, when they once again whip out Brown Eyed Girl or Unchained Melody. They used to be the best Christmas music station, with lots of Elvis and Beach Boys, but last year switched to crappy KOST music like the Carpenters and (shudder) Mannheim Steamroller.
KCSN - Can't really get the signal too well, but I still tune in Chuck Cecil's Swingin' Years every Sunday night 8-12. I believe it's the longest running radio program in the United States. Chuck is my favorite on-air announcer.
KLOS - This station has a dreary and dull playlist of classic rock. However, about once a year they do an A to Z that will knock your socks off. Some really obscure stuff is unearthed. The only other time I listen to them is maybe Sunday evenings when they play 4 albums all the way through.
KFWB - Gotta listen to the first three innings of any Dodger game to hear Vin Scully. Still not sure why he only does the first three...
KPCC - Good local talk show called "Air Talk" from 10-12. On Friday they review films in a segment called Film Week. Prefer KPCC to KCRW, which is unbelievably snooty.