We knew our son was ready for a "big boy bed" because he was good at following instructions, he went to sleep easily without issues when we did the bedtime routine, and he was starting to potty-train so it seemed like a good time. We were right. We had one night of him getting up and such, and we sat down and explained the rules to him, and that was that.
Our daughter began climbing out of her crib at 15 months old. We knew she was NOT ready for a big bed yet, so we got sleep-sacks to make climbing out too difficult. Other friends have gotten tents. She is now 27 months old, and still not even close to ready. She just doesn't follow instructions that well, and when something interesting is going on downstairs, she doesn't go to sleep right away. We know if we moved her now, she'd be up and down like a jack-in-the-box. She DOES have her own pillow, though.
Hope this helps!