This was written in the asoiaf.westeros.org forums in 2006, and it's the best thing ever:
"I have a crackpot theory that Sandor Clegane and The Mountain are actually brothers. I'm trying to ferret out the proof in the text....and it's been a slow and arduous process (Hooked-On-Phonics says I'm at a 6th grade reading level)...but I think I'm gradually finding the link.
Granted, I'm not an expert like y'all when it comes to "logic" or "making connections" or "thinking rationally" but I think I finally have stumbled onto the biggest linkage in the entire series. Please, before you shout me out...all I ask is that you read my theories. I've done weeks of research on this...I've even sent my results off to MIT (which I can only assume they're processing as we speak) and I have been sober for at least 14% of the time.
1)I know it sounds crazy..but I think there's evidence to back this up. Like for example, I noticed they both had very similar last names: Clegane. It got me thinking for several hours...why would they have such similar last names??? Who has similar last names? Well the first thing I thought was...married people. And then I spent a couple days ruminating on whether they were married or not. But I didn't think gay marriage had come to Westeros yet...so I went back to my chalk board, and put on my thinking cap and pondered some more over my elaborate multi-tiered equations. And then I thought, "Hey wait, fathers generally have similar last names to their sons!" And that seemed like a surefire truth. But then I thought the Hound was a virgin...because he hits on little girls...so he couldn't be the father. So I went into my basement...and starting mixing various chemicals in my Chemistry set.....and when the mixture turned blue, I thought "Eureka!" What if they were brothers! That would explain why the Hound kept talking about killing his brother!! I just thought he meant Ned Stark the whole time, because they seemed so similar. Ned Stark was the hand and Sandor Clegane had hands.
2) Both Gregor and Sandor have kidnapped Arya at various times in the book. Now, why would characters kidnap that hellbitch if they didn't share similar DNA?
3) But then I thought, George RR Martin is very subtle. Like I realizd that maybe Mya Stone was King Robert's daughter even though her last name wasn't Robert. So I figured if he wanted us to figure this out, he'd hide it within their names. Check this out. Gregor is an anagram of Gorger. Sandor is an anagram of Radons. Coincidence? Well, sure, possibly...but if it looks like a rat and smells like a rat, it's probably a cat.
4) Both enjoy long walks by the beach, evenings with friends, and disembowling children.
5) And last but not least, Pg. 544 ASOS U.S. Edition.
It wasn't the first time he [sandor] had talked of killing the Mountain. "But he's your brother," Arya said dubiously.
Now I admit, this one confused me. Why would Arya think a mountain was Sandor's brother? Are they both some form of geological formation? I haven't ruled that out either. And how do you kill a mountain? I mean I guess you could punch it really hard..but I don't know if that will work. I hate mountains too. All big and rocky..and high. Maybe I'll kill one once I get done with this thread.
I forget what my point was, but I did have one. And it was a whopper!
Feel free to try to rip apart my logic all you like. You'll feel pretty dumb when those results come back from MIT."