Basically, there is nothing wrong with third party batteries just make sure you buy known ones. The best brands are Hahnel and Delkin. They are more expensive than the eBay cheapies but much much better.
I have read (here) that the D3100 prevents use of 3rd-party batteries. If they don't work, you should be able to get a refund. While I agree that there's nothing much wrong with 3rd party batteries, I also think that I'm not going to buy more than one or possibly 2, so the difference may not matter so much.
My refurbished D80 came with a 3rd party battery, and I bought a second 3rd party battery for it. I sold it with one of the batteries, but the battery that I kept did not work in the D300s that I have now. It was a reputable make - Delkin Devices. I now have 2 Nikon batteries for the D300s.