I'm on a big twin website and I've seen people do it all ways and succeed. In my house, we converted the girls cribs to toddler beds when they were 20 months old in conjunction with moving. They hadn't climbed out and didn't have problems with the cribs, but WE the adults were ready. (so - to answer your question, I didn't have any problems moving my kids before they fought their cribs)
We didn't move to twin beds until they were 4. No real reason... they seemed happy in the toddler beds so we waited until we redecorated their room. If I had had to buy toddler beds, I would not have done it - they could have gone right to twin beds at 20 months. But since it was easy, we tried the toddler beds and I'm glad we did because one of my daughters rolled around a lot and would have fallen out if she didn't have that little railing on the side.
I have several friends on the twin website who moved one child to a toddler bed and left the other in the crib for months or even a year. It seemed to work just fine for them.
I did want to add that I agree with Hannah, it seems that the earlier people move their kids to toddler/big kid beds, the easier the transition. It's like kids don't realize at age two that they can get up and wreck the room, so they don't. But if they switch closer to three or four, they get excited about the freedom and run around at nap and bedtime.