My first character ever, an Argonian ran with Hadvar. He hated the Stormcloaks for obvious reasons (note: When I first did this, I had no idea Windhelm was forcing Argonians to stay outside the city), so he ran with the Legion.
Following Alvor's instructions to the letter, he ran to Windhelm and helped some of the Companions slay a giant along the way. He then went into Bleaks Falls Barrow with the Dark Elf companion he hired in 'The Drunken Hunter' shop. The poor lass died and he soldiered on. I suspect she was hitting on him with a comment about how he was much like her. This saddened him, as he would've considered marrying her.
He reclaimed the Golden Claw and the Dragon Tablet and escaped. Then he went to Jarl Baalgruf who told him to slay a dragon. He did so.
His little adventure ended abruptly in a cave of Falmers.
