Playable races are as follows. Each race has a specific set of modifications that they make to your character.
Players Handbook Races (good for inexperienced players)
Human: Humans get an extra feat at first level, and gets 4 bonus skill points at level 1, and 1 more at every level thereafter.
Dwarf: +2 Constitution, -2 Charisma. Dwarves can see in the dark for short distances, are resistant against magic and poison, have special training against goblinoids and giants, and have advanced stonecunning abilities.
Elf: +2 Dexterity, -2 Constitution. Elves do not have to sleep, and can see in dim light, have super-human perception skills, and are automatically proficient with bows, rapiers, and longswords. Elves are also resistant to enchantments.
Gnome: +2 Constitution, -2 Strength. Gnomes are small, meaning that they must use smaller weapons, smaller armor, and smaller mounts. Gnomes can see better in low-light then humans, are resistant to illusions, have training against giants, have keen ears, and a slightly attuned sense of smell which aids them in Craft (alchemy). Gnomes with charisma of 10 or higher can also cast a small amount of illusion spells for free once per day.
Half-Elves: They suck. plain and simple. Slightly increased sensory perception, and slight bonus to negotiation skills. The Wizard's community agrees.
Half-Orc: +2 Strength, -2 Intelligence, -2 Charisma. Half-Orcs can see in the dark for short distances.
Halflings (hobbits): +2 Dexterity, -2 Strength. Halflings are small, like gnomes. Halflings are good jumpers and climbers, and are light of foot. Halflings are also supernaturally good at avoiding trouble (bonus on all saving throws), are resistant to fear, have keen ears, and are good at throwing things.
Anthropomorphic Races: (intermediate-advanced players)
Anthropomorphs, sometimes called "furries" are humanoids with animal characters, or animals with human characteristics. note: I will only list animals that are playable as first level characters.
Bat: -4 Strength, +6 Wisdom, -2 Charisma. Bats are small, like gnomes. While bats have poor vision, they compensate with advance echolocation which allows them to locate objects withing 120 feet of them. They also maintain the ability to fly.
Lizard: -4 Strength, +2 Dexterity, +4 Wisdom, -4 charisma. Lizards are small, like gnomes. Lizards can use their dexterity to climb instead of their strength, and have excellent ballance. Lizards maintain the ability to use their bite as a weapon.
Monkey: -4 Strength, +2 Dexterity, +4 Wisdom, -2 charisma. Monkeys are small, like gnomes. Monkeys can use their dexterity to climb instead of their strength, and have excellent ballance. Monkeys maintain the ability to use their bite as a weapon.
Rat: -4 Strength, +2 Dexterity, +4 Wisdom, -4 charisma. Rats are small, like gnomes. Rats can use their dexterity to climb instead of their strength, and have excellent ballance. Rats are also extrwemely stealthy. Rats maintain the ability to use their bite as a weapon.
Raven: -6 Strength, +2 Dexterity, +4 Wisdom, -4 charisma. Ravens are small, like gnomes. Ravens maintain the ability to fly, and the ability to use their claws as weapons.
Toad: -4 Strength, -2 Dexterity, +6 Wisdom, -2 Charisma. Toads coloration makes it easier for them to hide.
Weasel: -4 Strength, +2 Dexterity, +4 Wisdom, -4 Charisma. Weasels are light-footed, so they are good at moving silently. Weasels also have the ability to cling to opponents with their teath and deal continuous bite damage.
Other Races (experienced players)
Changeling: Changelings are resistant to sleep effects, are cunning speakers, and are natural linguists (speak language is a class skill). They also have the ability to alter their physical appearance to aid in disguises.
Dwarf, Deep: Deep dwarves are more resistant to magic and posion then standard dwarves, and can see further in the dark, but are sensitive to sunlight.
Dwarf, Mountain: mountain dwarves live further underground then standard Dwarves, but not as deep as Deep Dwarves. Only minor appearance differences.
Elf, Aquatic: +2 Dexterity, -2 Intelligence. As the name suggests, aquatic elves live primarily under water, but they can survive above water for 1 hour per point of constitution. Aquatic elves are also excellent swimmers. Aquatic elves can see further in low light then regular elves.
Elf, Gray: -2 Strength, +2 Dexterity, -2 Constitution, +2 intelligence.
Elf, Wild: +2 Dexterity, -2 Intelligence.
Elf, Sylvan: +2 Strength, +2 Dexterity, -2 Constitution. -2 Intelligence, -2 Charisma.
Goblin: -2 Strength, +2 Dexterity, -2 Charisma. Goblins have light feet, allowing them to move more quietly.
Halfling, Tallfellow: Tallfellows are not as good at jumping or climbing, and are not as quiet as standard halflings. Tallfellows have increased perception ability.
Kenku: +2 Dexterity, -2 Strength. Kenku resemblue humanoid ravens. Kenku are skilled at working in groups, even in combat. Kenku can mimick the voices of other beings, have clas which can be used as weapons (weaker then daggers, but a lot harder to lose), are naturally stealthy, and can see in low-light conditions.
Kobold: -4 Strength, +2 Dexterity. Kobolds resemble humanoid lizards, and are said to be deistant descendants of dragons. Kobolds are sensitive to light, and take penalties when fighting in direct sunlight. Kobolds are excellent trapmakers, and miners, and are good at searching.
Orc: +4 Strength, -2 Intelligence, -2 Wisdom, -2 Charisma. Orcs can see in the dark for short distances, but are light sensitive.
Shifter: +2 Dexterity, -2 Intelligence, -2 Charisma. Shifters are distant decendants of lycanthropes who can call on small ammounts of lycanthropic power for a short time. Shifters are also well-balance, and good at climbing and jumping.
Warforged: +2 Constitution, -2 Wisdom, -2 Charisma. Warforged are animated constructs. They cannot wear armor (they have armor built into their bodies), but can enhance their "skin" like any other type of armor. They are also resistant to critical hits. As living constructs, they do not eat, sleep, drink, or grow tired, and are immune to poison, disease, and paralysis.
Warforged Scout: +2 Dexterity, -2 Strength, -2 Wisdom, -2 Charisma. Scouts are small, like gnomes. See warforged entry for other details.