I've moved twice with all of my furniture and it's still going strong. The only thing that worries me for my next move would be the board on the back of my bookshelf, since it's only held in with very tiny nails.
If I understand which board you're talking about (a thin hardboard on the back), I'm usually not worried about that one - I have a stockpile of nails available, and I could probably reinforce it with something I have on hand if the edges degrade too much. My problems are usually that driving screws and other fasteners sometimes damages the material, making the connection single-use only. It's fixable to some extent with adhesives, but once you start pouring glue down the shafts, the whole thing becomes that much harder to disassemble in the future.