Are we talking movies? I'm guessing so considering this is in the movie board.
Growing up Iron Man was my absolute favourite super hero - and also growing up RDJ was my favourite actor. You can imagine my excitement when he popped up at the end of the Norton Hulk movie and was announced as Iron Man.
Based on that I'd have to say Pro-Reg. It has my hero on it, how could he be wrong?
Getting into his mindset, he accidently created things, enemies, ultron - things that had the capacity to destroy the world or kill a lot of innocent people. He's scared of his own ability. He's done this and he's a good guy.
Now imagine a person just like Iron Man, they'd only need a fraction of his talent and they'd be able to do horrific things if they wanted. Stark is scared of the unknown. He knows what he's capable of and he knows what others are capable of too. He's bullied his mind into the pro-reg side.
I don't think it suits his character, to be pro-reg. This is why it's hard to take a side because I think if Stark had a healthy mind he'd be anti-reg.
I won't get into the comic book side as it's likely going to be very different and I don't want to spoil anything.
I recommend picking up a copy of civil war, it's a short read and one of my favourite arcs.