When does a baby begin to use a toddler bed?

When they can climb out of their crib and it is no longer safe.

My ds never ever tried to climb out of his crib. We started gradually introducing him to a bed (just a regular twin) at about 2 years and by 28 months he was sleeping in his with a bed rail on it.
I would suggest that even if they aren't climbing that they don't sleep in a crib past 2-2.5...they need that independence of getting in and out of bed.

My daughter is almost 19mths, she never tried to climb out of the cot but she wouldn't go to sleep in it, she preferred our bed.

One sleep deprived mum & dad took the slide side off her cot, she now has the freedom to get in and out of her "own bed" and she is sleeping much better too, I guess she no longer feels trapped by bars.

My older children (girl 9yrs & boy 7ys) were around 16 to 20 mths when the decide they no longer like the cot and moved into beds.

You just know by little changes in there bed time behaviour that it is time to move into a bed, our kids did anyway.

Good Luck