For example, if the zoning for property changes from residential to commercial, or if an owner is able to obtain a special use permit (or some other kind of variance), then the tax basis for that property might change. Typically the tax basis will increase for zoning changes like the one I described earlier, because a parcel of land that's zoned commercially is worth more than it would be if it were zoned residentially.
New purchases aside, permitted improvements are the most common trigger for tax increases via the supplemental tax process.
While under Proposition 13 the property tax rate is fixed at 1% of assessed value, in actuality, as the market value of your home increases so will your assessed value. This will certainly result in incremental tax increases each year. This incremental cost will be in addition to amounts required to repay any assessment bonds approved by the voters.
Your property tax bill actually consists of 3 separate levy categories:
1) General Tax Levy - controlled by Proposition 13, this tax is limited to a maximum of 1% of the assessed value of your property (the "land" and "improvements"), and can be no more than 2% greater than the previous year's tax bill.
2) Voter Approved Indebtedness - includes taxes levied to repay bonds approved by the voters. This amount varies from county to county depending upon the number of local bond issues approved. Under current law, local general obligation bonds require a 2/3rds majority vote to pass.
3) Direct/Special Assessments - now controlled by Proposition 218, these assessments require a majority vote of the property owners, with each owner voting the dollar amount of their assessment. Fees charged for the property-related services of sewer, water, and refuse collection can be imposed without a vote, but may not be greater than the cost of providing the service.
While your question focuses on what drives property tax increases, you may also find the following information quite interesting as well:
Prop 8 allows individual homeowners to submit their own request for property tax reassessment. After any Prop 8 reassessment, your property assessment can change upwards at an accelerated rate faster than the CA's constitutional 2% cap normally expected, and will only occur at this accelerated rate until your property has reached the before-prop8 reassessment level.
Because of Prop 13, once you buy a home, your property taxes remain constant UNLESS you add square footage. At that point, you home is reassessed and your taxes increase by the value of the extra feet you added. This is not a reset of your entire property tax base: your EXISTING tax base is considered and your additional square footage is calculated at your EXISTING tax rate. Unless you do some SERIOUS additions, you will not likely see much of a change.
Tax assessments against properties are not seen in a good light by local officials and therefore are not likely to happen.