A whole lot, but I've got you by a couple of decades and I'm lucky enough to have lived my life about an hour outside of L.A. so there are lots of opportunities. I'll just list some favorites and ones that feel historically noteworthy off the top of my head.
My first show was a Jefferson Airplane reunion, but I barely remember it. I was around 6 or 7. Second was The Thompson Twins.
Pavement (x7), Frank Black (x4), Elliott Smith (x3), Paul Simon (x3), Bob Dylan (x2, cool box to check and all, but they were not good shows), Springsteen, McCartney, Elvis Costello (x4), Sebadoh (x2), Folk Implosion, Beck (x2), the Shins (x2, before they stopped being good), Built to Spill (x2), Elastica, Sonic Youth (x3) Lollapalooza w/ AiC, Primus Rage Against the Machine, many more, the Pixies, the Breeders (x2), Radiohead. Tom Waits, Fiona Apple, Wilco, the National, Sufjan Stevens, Dave Matthews (bad show, left early), Beastie Boys (terrible show, left early), RHCP (even worse, definitely left early), Porno for Pyros (worst show I've ever seen, including more than a couple local bands that weren't ready for the stage, for some reason stayed til they were done), plus many, many more.
Some of my favorites that won't mean much to many Dr. Dog, Delta Spirit, Franklin for Short (roughly 1,000 times), the Spires, Margot and the Nuclear So and Sos w/ Dinosaur Feathers, Tapes n Tapes, the Black Heart Procession, Tall Tales and the Silver Lining, Jeremy Enigk/Imaad Wassif, the Silver Jews