I have two different bottom boards (the boards on the bottom:) on my hives. Simple solid boards and screened bottom boards. Supposedly the screened bottom boards are good for two reasons: they allow for better circulation in the hive and they allow any "mites" to fall through to the ground and therefore it is more difficult for them to climb back on the bees. Here is a picture of my two hives on the stand with two different bottoms.
The one on the right is solid and the one on the left is screened. Notice that the bees are huddled near the entrance on the right - they are actually trying to cool off the hive in the blistering heat we had today. So - it looks like the screened bottom board is working!