Well the obvious answer is "when they're ready". :) For my kids that's been different each time. The earliest was around 18 months, the latest was closer to 3. I'm in the process of transitioning my 22month old to a toddler bed. She climbs in and out of her crib easily, so there's really no point in keeping her in it.
The hard part is like you said, keeping her there when there are other things to play with. This is when you set up a bedtime routine, like reading a book or two before lights out. I usually cuddle for a little while too, until she's almost asleep and then leave. Some nights it works, some nights she's back in her crib, mostly because it's familiar, and the big bed isn't.
Some of my kids needed a transitional period, some went straight to the big kid bed without a 2nd thought.