Strictly speaking, the Sun and the Moon are considered to be luminaries, not planets. In astrology, Earth is not included in the birthchart since it is geocentric, though astrologer, Cynthia L. C. Wood argues for the validity of inserting earth into our birthcharts (Earth and Taurus: Geocentric Astrology's Missing Link, The Mountain Astrologer; Issue 142 - Dec/Jan 2009).
The planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto are included in a typical birthchart. Some astrologers also insert Chiron - a minor planet located between Mars and Jupiter, into birthcharts. Pluto, although no longer deemed to be a planet scientifically, still offers valuable insight astrologically. It was discovered and included in the solar system for a reason.
Here are the basic meanings for each planet/luminary:
Sun: Will power, destiny, male authority figures, what's centrally important to you
Moon: Feelings and emotions, habits, the past, mother, female figures, nurturance, sensitivity
Mercury: Communication, thinking style, dexterity, mental images, ideas
Venus: Love, charm, arts, luxury, values, possessions, relationships
Mars: Assertion, wars, weapons, courage, bravery, determination
Jupiter: Expansion, religion, philosophy, foreign travels
Saturn: Tradition, structure, old father time, restriction, limitation, boundary
Uranus: Revolution, changes, groundbreaking ideas, eccentricity
Neptune: Creativity, dreams, imagination, illusion, vagueness, lack of boundary
Pluto: Transformation, psyche, elimination, exposure, hidden factors