What are the advantages/disadvantages of each race?

Argonian

• +10 Lockpicking, +5 Restoration, Alteration, Light Armor, Sneak, Pickpocket
• 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.

Breton

• +10 Conjuration, +5 Alchemy, Illusion, Restoration, Alteration, Speech
• Dragonskin : Absorb 50% of magicka from hostile spells for 60 seconds.
• Magic Resistance : Breton blood grants a 25% resistance to magic.

Dunmer (Dark Elf)

• +10 Destruction, +5 Alchemy, Illusion, Alteration, Light Armor, Sneak
• 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)

• +10 Illusion, +5 Conjuration, Destruction, Restoration, Alteration, Enchanting
• Highborn : Regenerate magicka faster for 60 seconds.
• Highborn : High Elves are born with 50 extra magicka.

Imperial

• +10 Restoration, +5 Destruction, Enchanting, Heavy Armor, Block, One-Handed
• 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.

Khajiit

• +10 Sneak, +5 Alchemy, One-Handed, Archery, Lockpicking, Pickpocket
• Night Eye : Improved night vision for 60 seconds.
• Claws : Khajiit claws do 15 points of damage.

Nord

• +10 Two-Handed, +5 Smithing, Block, One-Handed, Light Armor, Speech
• Battle Cry : Target flees for 30 seconds.
• Resist Frost: Your Nord blood gives you 50% resistance to frost.

Orsimer (Orc)

• +10 Heavy Armor, +5 Enchanting, Smithing, Block, Two-Handed, One-Handed
• Berserker Rage : You take half damage and do double damage for 60 seconds.

Redguard

• +10 One-Handed, +5 Destruction, Alteration, Smithing, Block, Archery
• Adrenaline Rush : Stamina regenerates 10x faster for 60 seconds.
• Resist Poison : Your Redguard blood gives you 50% resistance to poison.

Bosmer (Wood Elf)

• +10 Archery, +5 Alchemy, Light Armor, Sneak, Lockpicking, Pickpocket
• 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.

source: http://www.reddit.com/r/skyrim/comments/m0e2a/complete_list_of_skyrim_race_differences/

It seems to me that the playstyles fall into 3 different categories: Warrior, Mage, and Assassin the warrior races are Orc, Nord, Redguard and Imperial. The mage races are Altmer, Dunmer and Breton.

The assassin races are Khajiit, Argonian, Bosmer. They each specialize into a certain part of that category like in the assassins the Khajiit is the best for sneaking up behind and slitting their throats, while the Argonian is best at robbing people and the Bosmer is best at sniping from a distance with arrows.

For warriors the Orc is best in armor while the Nord is best at slow strong two handed weapons and Redguards are best at faster weaker one handed weapons.

Altmer is the best all around mage while Dunmer are the best at strong quick magic kills and Breton are best at summoning allies at your assistance.

This is entirely based off of their starting stats and skills. Though in the game if you wanted you could make a Nord do a Altmers job if you truly wanted to.