There are a few achievements tied to the main quest which have you joining either the Stormcloaks OR the Imperial Legion, but these are awarded for picking either path, rather than siding with one group over the other (as in Dragon Age: Origins, for instance).
All of these achievements should be attainable in a single playthrough:
Unbound (10g) - Complete "Unbound"
Bleak Falls Barrow (10g) - Complete "Bleak Falls Barrow"
The Way of the Voice (20g) - Complete "The Way of the Voice"
Diplomatic Immunity (20g) - Complete "Diplomatic Immunity"
Alduin's Wall (20g) - Complete "Alduin's Wall"
Elder Knowledge (20g) - Complete "Elder Knowledge"
The Fallen (20g) - Complete "The Fallen"
Dragonslayer (50g) - Complete "Dragonslayer"
Take Up Arms (10g) - Join the Companions
Blood Oath (10g) - Become a member of the Circle
Glory of the Dead (30g) - Complete "Glory of the Dead"
Gatekeeper (10g) - Join the College of Winterhold
Revealing the Unseen (10g) - Complete "Revealing the Unseen"
The Eye of Magnus (30g) - Complete "The Eye of Magnus"
Taking Care of Business (10g) - Join the Thieves Guild
Darkness Returns (10g) - Complete "Darkness Returns"
One with the Shadows (30g) - Returned the Thieves Guild to its former glory
With Friends Like These... (10g) - Join the Dark Brotherhood
Bound Until Death (10g) - Complete" Bound Until Death"
Hail Sithis! (30g) - Complete "Hail Sithis!"
Taking Sides (10g) - Join the Stormcloaks or the Imperial Army
War Hero (10g) - Capture Fort Sunguard or Fort Greenwall
Hero of Skyrim (30g) - Capture Solitude or Windhelm
Sideways (20g) - Complete 10 side quests
Hero of the People (30g) - Complete 30 Misc Objectives
Hard Worker (10g) - Chop wood, mine ore, and cook food
Thief (30g) - Pick 50 locks and 50 pockets
Snake Tongue (10g) - Successfully persuade, bribe, and intimidate
Blessing (10g) - Select a Standing Stone blessing
Standing Stones (30g) - Find 13 Standing Stones
Citizen (10g) - Buy a house
Wanted (10g) - Escape from jail
Married (10g) - Get married
Artificer (10g) - Make a smithed item, an enchanted item, and a potion
Master Criminal (20g) - Bounty of 1000 gold in all nine holds
Golden Touch (30g) - Have 100,000 gold
Delver (40g) - Clear 50 dungeons
Skill Master (40g) - Get a skill to 100
Explorer (40g) - Discover 100 locations
Reader (20g) - Read 50 Skill Books
Daedric Influence (10g) - Acquire a Daedric Artifact
Oblivion Walker (30g) - Collect 15 Daedric Artifacts
Dragon Soul (10g) - Absorb a dragon soul
Dragon Hunter (20g) - Absorb 20 dragon souls
Words of Power (10g) - Learn all three words of a shout
Thu'um Master (40g) - Learn 20 shouts
Apprentice (5g) - Reach Level 5
Adept (10g) - Reach Level 10
Expert (25g) - Reach Level 25
Master (50g) - Reach Level 50