California voted to the left of the nation when Democrats lost for years:
1972: 55-41 Nixon vs 60-38 Nixon nationwide
1984: 57-41 Reagan vs 59-40 Reagan nationwide
1988: 51-47 Bush vs 53-45 Bush nationwide
However, California ran to the right of the nation when Democrats won:
1960: 50-49 Nixon vs. 49-49 Kennedy nationwide
1964: 59-41 Johnson vs 61-39 Johnson nationwide
1976: 49-47 Ford vs 50-48 Carter nationwide
The only time California ran to the right of the nation in my lifetime was in 1968:
1968: 47-44 Nixon vs. 43-42 Nixon nationwide
One reason for these results is that from 1960 to 2008, California was THE battleground state. There were many books that spoke of this. As a kid interested in politics, I remember reading a book around 1971 from my public library that predicted that the Democrats would beat Nixon; it predicted that the Southern states would return to the Democratic fold, and that "California would be THE battleground for 1972"; it would be where the election would be decided.
Was any election "decided" by California? One could argue that the 1968 Presidential election was. Nixon carried California by a mere 3 points, and HHH was surging on Election Day. A shift of 1.5% of the votes in California to HHH would have thrown the election into the Electoral College, where it would have become interesting. That didn't happen, but what if it had? I would state, however, that this was the ONLY time that California was, truly, a "tipping point" state of any kind.
California was the tipping point state in 1916, which Wilson won by 3,773 votes. It was not the tipping point in 1968, though I suppose it did have the potential to be if a few other states like Illinois and Ohio had not been closer than California.