A few opportunities are outlined below. Several universities and research groups maintain active lists of fellowship opportunities for undergraduates, graduate students, and postdocs - be sure to check those out.
University databases - Columbia, Cornell, Duke, Harvard, and UCLA
Undergraduates - Beckman Scholars
Graduate students - NSF Graduate Research Fellowship, National Defense Science & Engineering Fellowship, Hertz Fellowship, Campos Group, Landry Lab
Postdocs - NIH F32 Fellowship, Helen Hay Whitney Fellowship, Arnold O. Beckman Postdoctoral Fellowship, Life Sciences Research Foundation, Landry Lab, Berkeley Sponsored Programs Office