The most common way that a term in the Legislature ends is that that the term ends and the officeholder leaves office. But there are a handful of other options:

Resignation
There have been about 255 resignations since 1849, most recently in January 2015.

Death
83 California Legislators have died in office, most recently in 2010.

Contested Seat
A seat is “contested” when one candidate is sworn into office and another candidate makes a claim that they were the actual winner. This happened most frequently when it took a while to get to Sacramento and candidates had to leave before the final vote tally arrived. When the second candidate won in the final count, they would present the evidence of their victory to that house of the legislature and a committee would determine who had actually won. Seven legislators lost their seats by having their elections contested; the most recent was in 1981.

Seat Declared Vacant
For many years, California law said that officerholders were required to remain within their jurisdiction during their term of service. Leaving the state during the term of your office (which current legislators now do regularly) meant surrendering your right to hold that office. Although it happened several times in statewide offices, this only happened once in the Legislature. In 1853, Assemblyman Horace W. Carpentier left the state and his seat was declared vacant. Don’t worry, it wasn’t too big a political setback; he soon became Oakland’s first mayor.

The Recall
The recall was introduced in California in 1911, since then four legislators have lost their seats in recall elections. Two immediately after the introduction of the recall (1913 and 1914) and twice in 1995.

Removal from Office
Removal from office has only happened once, in 1995, when Dick Mountjoy was reelected to the Assembly at the same time he was elected to the State Senate in a special election. A majority of the membership in the Assembly determined that the Senate election took precedence, and Mountjoy was removed from office as an Assemblyman. (Added 3/30: After reviewing official sources, it looks like Mountjoy was not removed from office, but was instead “disqualified” from assuming office in the 1995-96 Session). Always important to remember that unlike the State Senate, the Assembly does have a period every two years when there are zero members in office.

Expulsion
Expulsion occurs when a house of the Legislature determines that a member has so significantly violated the public trust that they are unfit to remain in office. There have only been five expulsions in state history, most recently in 1905 when four State Senators were found guilty of having accepted bribes. In 2014, Senators Knight, Anderson, and Vidak introduced SR 29, to expel Rod Wright from the State Senate. Coincidentally, if SR 29 had passed, Wright would have been the second Senator Wright to be expelled from the Senate (Eli Wright was one of the four expelled in 1905).