Sydney's 10mm "Ultra" SMG

The weapon used by the relic hunter Sydney. It can be looted from her by pick-pocketing, waiting for her to die, or killing her yourself. This weapon can also be acquired from finding a note within the ruins of the hotel in the quest Reilly's Rangers. During the mission, be sure to check the side rooms until you find a skeleton on one of the beds. You'll find an assault rifle under the bed, some ammo next to it, and the note on the bed next to the corpse. Go back to Sydney after finding it in Rivet City and she will tell you it was from her father, that he was attempting to make one big deal and set her up for life, but was double crossed. Realizing she was wrong about her father, she will give you the gun. Note however that this can only be done AFTER returning the Declaration to Washington. After speaking to her in Rivet City, she will move to Underworld and become a weapons merchant there.

There is a bug/exploit that allows you to receive her ultra SMG in perfect condition (along with 50 rounds of 10mm ammo) as many times as you want. After receiving the gun once, the dialogue option to inform her of her father's recording vanishes, but by asking her about herself, then asking about her gun, then her father, this option reappears and you can once again deliver his message and receive the reward. There is seemingly no limit on the number of times this can be done.

Edit: I am doing this on the PS3(Confirmed to work on 360 version also) and the exploit goes like this: Start a conversation with Sydney: Since we're done now, why don't you tell me about yourself? Nice gun. I've never seen one like that. That's all for now, I guess (this just takes you back one level in the convo tree) So, whatever happened to your father? Sydney, I found a note from your father. He didn't abandon you.

Rinse and repeat ;)