Here is a list of the differences between the races in Skyrim and a general overview of their skills, powers, etc.
Skill Bonuses: +10 Lockpicking, +5 Restoration, Alteration, Light Armor, Sneak, Pickpocket
Racial Power: Histskin : Invoke the power of the Hist to recover health ten times faster for 60 seconds.
Resist Disease: Your Argonian blood is 50% resistant to disease.
Water Breathing: Your Argonian Lungs can breath underwater.
Skill Bonuses: +10 Conjuration, +5 Alchemy, Illusion, Restoration, Alteration, Speech
Racial Power: Dragonskin : Absorb 50% of magicka from hostile spells for 60 seconds.
Magic Resistance: Breton blood grants a 25% resistance to magic.
Dunmer (Dark Elf)
Skill Bonuses: +10 Destruction, +5 Alchemy, Illusion, Alteration, Light Armor, Sneak
Racial Power: Ancestor’s Wrath : For 60 seconds, opponents that get too close take 8 points per second of fire damage.
Resist Fire – Your Dunmer blood gives you 50% resistance to fire.
Altmer (High Elf)
Skill Bonuses: +10 Illusion, +5 Conjuration, Destruction, Restoration, Alteration, Enchanting
Racial Power: Highborn: Regenerate magicka faster for 60 seconds.
Racial Abilities: Highborn: High Elves are born with 50 extra magicka.
Skill Bonuses: +10 Restoration, +5 Destruction, Enchanting, Heavy Armor, Block, One-Handed
Racial Power: Voice of the Emperor: Calms nearby people for 60 seconds.
Imperial Luck: Anywhere gold coins might be found, Imperials always seem to find a few more.
Skill Bonuses: +10 Sneak, +5 Alchemy, One-Handed, Archery, Lockpicking, Pickpocket
Racial Power: Night Eye: Improved night vision for 60 seconds.
Claws: Khajiit claws do 15 points of damage.
Skill Bonuses: +10 Two-Handed, +5 Smithing, Block, One-Handed, Light Armor, Speech
Racial Power: Battle Cry: Target flees for 30 seconds.
Resist Frost: Your Nord blood gives you 50% resistance to frost.
Skill Bonuses: +10 Heavy Armor, +5 Enchanting, Smithing, Block, Two-Handed, One-Handed
Berserker Rage: You take half damage and do double damage for 60 seconds.
Skill Bonuses: +10 One-Handed, +5 Destruction, Alteration, Smithing, Block, Archery
Racial Power: Adrenaline Rush: Stamina regenerates 10x faster for 60 seconds.
Resist Poison: Your Redguard blood gives you 50% resistance to poison.
Bosmer (Wood Elf)
Skill Bonuses: +10 Archery, +5 Alchemy, Light Armor, Sneak, Lockpicking, Pickpocket
Racial Power: Command Animal: Make an animal an ally for 60 seconds.
Resist Disease and Poison: Your Bosmer blood gives you 50% resistance to poison and disease.
Every character starts with these two spells:
Flames : A gout of fire that does 8 points per second. Targets on fire take extra damage.
Healing : Heals the caster 10 points per second.
Breton's also start with...
Conjure Familiar : Summons a Familiar for 60 seconds wherever the caster is pointing.
Dunmer also start with...
Sparks : Lightning that does 8 points of shock damage to health and magicka per second.
Altmer also start with...
Fury : Creatures and people up to level 6 will attack anything nearby for 30 seconds.