I assume the transfer will be categorized as a gift - will I have to pay a gift tax?
Gift taxes are paid by the party or estate bestowing the gift. Your parents can look here for more information on gift taxes: http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Frequently-Asked-Questions-on-Gift-Taxes
They may also need to file a gift tax return: http://www.irs.gov/pub/irs-pdf/f709.pdf
For your part, you will want to keep accurate records of what your parents paid for the property and any improvements. This will be useful later when you sell it.
I will add only one other comment; and, that is that this change in ownership will not trigger a reassessment for property tax purposes.
When you record the deed, you should file a Preliminary Change of Ownership Report (PCOR) form BOE-502A, on which you check the boxes on C. on Part 1 on the first page to indicate that this is a transfer between parent(s) and child(ren). Below is a link to the LA County Assessor's form page.
You will also need to file a Claim for Reassessment Exclusion for Transfer Between Parent and Child, form BOE-58-AH, OWN-88 with the assessor. The assessor may send you this form. There are time limits on filing this form, so if the assessor does not send you one, get your own form, print your own form from the assessor's webpage and complete and file it with the assessor.
As to gift tax, your parents should prepare a federal gift tax return, but highly unlikely any gift taxes would be owed. As of 2013, a person could make lifetime gifts of $5,250,000, before owing any gift taxes. California does not have a state tax on gifts.
This office is licensed to practice law only in the state of California. The answer provided above is for general information only, is not intended and should not be taken as specific legal advice and does not create an attorney client relationship with the party making the inquiry.