Amy's childhood friend and sort of boyfriendfiancehusband. They might have had the longest night before their wedding ever, but Rory doesn't really mind. It was an enriching experience.
He grew up hearing stories of Amy's imaginary friend, the Raggedy Doctor, and though he never believed in them, he entertained the idea enough to dress up as him. Or quite possibly feared Amy enough not to say no
Rory started traveling with the Doctor after being swept off for a romantic escape with Amy in Venice, on the night before their wedding. He'd much rather life a quiet, peaceful life with Amy than go adventuring through time and space, but he can understand the appeal it holds for her, and if he's honest, the adventure is just as fun for him, too, as long as they'll settle down one day.
Even though he's grown to like the Doctor, he can't help feeling threatened by the adventure and excitement the man can offer--and by Amy's lifelong crush. Kissing him on the night before her wedding probably didn't help. Just because he's married to her now doesn't mean they've given up completely competing over her, every now and then.
It's possible he was swimming, had a time hiccup, and woke up in another universe.
But what really happened is that he slipped through one of brokenverse's tricky cracks, and ended up in the wrong universe.
...Except not. What really happened was that he was rebuilt as a plastic duplicate by the Nestine Consciousness and imprinted with the memories of Rory that Amy had, which inadvertently restored his soul in the process. Then he slipped through one of brokenverse's tricky cracks, ended up in the wrong universe, and was mistaken for a walking paradox.
Two universes, two lifetimes, and two thousand years later, everything finally worked out. He's neither plastic nor a paradox, though he holds memories of two lifetimes and two thousand years and two universes that never were, and now travels with the Doctor, his newly wed wife Amy, and the other strange characters they seem to keep on picking up along the way.