The Iron Throne is currently held by Joffrey Baratheon after Robert died under suspicious circumstances.
Current line of succession for the Iron Throne:
- Tommen Baratheon
- Halyn Baratheon (one of two kids Cersei and Robert Baratheon had before his death)
- Myrcella Baratheon
- Mary Baratheon (other kid of Cersei and Robert B)
- Stannis 'the Mannis' Baratheon
- Renly Baratheon
The Seven Kingdoms:
The North-
Current Ruler: Eddard Stark
Spouse: Catelyn Stark
Expected Heir: Jon Snow (...somehow. Robb's been castrated, Brandon and Rickon are both dead, Sansa will inherit if Jon dies before Ned, Arya's fourth in line behind Sansa's son Arnos Arryn)
The Vale-
Current Ruler: Harrold Arryn
Spouse: Sansa Stark
Expected Heir: Arnos Arryn
The Westerlands-
Current Ruler: Tyrion Lannister
Spouse: Alla Tyrell
Expected Heir: Joffrey Baratheon (No kids yet from Tyrion)
The Trident-
Current Ruler: Catelyn Stark (Long story. Her dad Hoster Tully dies of old age, Cat's brother Edmure takes over...for one week before dying in personal combat with Lyonel Frey during battle)
Spouse: Eddard Stark
Expected Heir: Sansa Stark
The Stormlands-
Current Ruler: Renly Baratheon
Spouse: Tyene Sand
Expected Heir: Joffrey Baratheon (same situation as Tyrion)
The Reach-
Current Ruler: Mace Tyrell
Spouse: Alerie Hightower
Expected Heir: Willas Tyrell
Dorne-
Current Ruler: Doran Martell
Spouse: Mellario
Expected Heir: Arianne Martell
Currently, the Seven Kingdoms are duking it out because Mace Tyrell is trying to press Viserys Targaryen's claim to the Iron Throne. Current lineup in this war is Mace/Doran/Catelyn (Team Viserys) versus Joffrey/Tyrion/Eddard (Team Joffrey).
After Robert Baratheon's death, Cersei Lannister would go on to marry Willas Tyrell. Meanwhile, Daenerys and Khal Drogo don't get hitched; instead, it's Daenerys and Jorah Mormont.