MP3 is a compressed format
MP3 is a compressed format. So any Wav file converted to MP3 is going to be compressed, meaning that it will loose some quality. If your question is at what point this is audible, then it all depends on how good you can hear and whether your MP3 listening device is of good enough quality for you to hear it. Generally speaking, 384kbps compression achieves a minimal level of compression w/o loosing too much data. In my opinion this is not audible on most home stereos.
Now for my MP3 player, I cut that down to 128kbps to save space. I use the player outdoors mostly and while I have a decent set of headphones, there is still a fair amount of outside noise that makes it into my ears, so the quality is not that important to me. That said, it's a pain to store multiple versions of the same file on my computer.