Postdoctoral Opportunities
The following are some useful resources for fellowships for a postdoctoral position.

Miller Research Fellowships, general eligibility, for postdocs at UC Berkeley.  Nomination deadline in early October.

Chancellor's Postdoctoral Fellowship, for students whose life experience, research or employment background will contribute significantly to academic diversity and excellence at the Berkeley campus. Application deadline in November.

NSF NATO Postdoctoral Fellowship, for citizens of NATO countries outside the U.S.  Deadline in early December.
A list of all NSF Postdoctoral Fellowships has other postdoctoral opportunities listed.

UC President's Postdoctoral Fellowship Program, for women and underrepresented minorities. Deadline in mid-November. Prior participation in outreach programs for underrepresented students is an important criteria for selection.
Berkeley also subscribes to two databases with funding opportunities:

Community of Science (COS) Funding Opportunities database

IRIS funding opportunities database