Not anymore. In the upcoming admissions season (those graduating high school in 2012 and college in 2016), subject tests are no longer required for the entire UC system. However, especially for a school as competitive as UCLA, they are strongly recommended because they can only strengthen your application. You will want to take advantage of every opportunity to show off your strengths as possible.
I don't get how Berkeley doesn't require them for engineering? I mean, won't its ranks go falling through the sky for engineering? Plus, correct me if I'm wrong, but I heard the UC system will require SAT II tests but NOT SAT I tests.
@gtfotu: I'm pretty sure it's the other way around... you have to take the SAT Reasoning Test (formerly called SAT I, or just the SAT), but you don't have to take the SAT Subject (formerly called SAT II).
Sat II are no longer required for the high school graduating class of 2012 and younger, however, it is recommended. Which means "take it", UCLA also wants those who intend to apply to engineering school to take the math II test, and a science subject test like physics, chem, or biology. The "recommended", is kind of like the "recommended" they use when saying "3 years of math required, '4 recommended'"
The UC governing leaders have long debated the use of SATs as a measure in determining eligibility -- many have felt that it compromises the educational system, primarily because it was felt to be an inequitable assessment. Every couple of years there's a proposal to discontinue the use of the SATs entirely. It's never gone that far, although these periodic evaluations and debates led to the ELC admissions some years back.
So it wasn't really much of a surprise, at least to me, that something would eventually "give" and it was done with the subject tests. Is this the end of it? Probably not.