Instead of trying to hail a taxi on the street, phone one of the many taxi companies. The Curb Taxi app allows for online hailing of L.A. taxis. The metered rate is $2.70 per mile, plus a $2.85 per-fare charge. Taxi rides from LAX have an additional $4 surcharge. Be aware that distances are greater than they might appear on the map so fares add up quickly.
On the other end of the price spectrum, limousines come equipped with everything from full bars to nightclub-style sound-and-light systems. Most charge by the hour, minimum hours sometimes required.