There's no exact time. Most children make the switch between the ages of 1½ and 3½ years old.
Naturally, you'll need to move your toddler to a bed once he or she has grown too big or become too active to sleep safely in the crib anymore. Once they are potty-trained, they'll also need to get out of the bed to use the (yay!) toilet.
Don't rush out and buy a new bed the day your toddler climbs out of the crib. He may not be ready to get out of a big kid's bed at night when everyone else is asleep. Lowering the crib mattress will buy you (and him!) some more time. Also, remove the padded bumpers once the climbing begins.
Have another baby on the way? If possible, try and make the switch 6-8 weeks before you are due. This lets your toddler settle in to his new bed before his crib gets "taken over."
Every kid is different. Some resist change. Some embrace it. Your firstborn will likely be very attached to the crib. (Can you blame her?). They feel a lot of pressure at this stage in their lives: Potty-training, Pre-School, eating habits, etc.
To ease the transition, here are a few tricks: put the new bed in the same place the crib used to be. (Or even place it in the room before he moves - so he can see it and get used to it.).
Get him excited about moving. Let him "help" you pick out the bed. Throw a "Big Kid" moving party. Make a big deal of it. (You can make him a Big Kid Bed Diploma here). Let him sleep with his old kid blanket, or buy him cool, new sheets.
Try different things. Be sure their new bed is a quality bed with adequate support. Old, family hand-me-downs are not the best things to induce quality sleep at night.
As in everything: encourage but do not punish. If they need the crib for a while longer, so be it. One thing we are sure of: he or she won't be a baby forever. Make the most of this precious time you have together.
(Thanks to babycenter.com for some of the helpful information above.)