Any format conversion is going to reduce the quality to some degree. How much depends on the differences in the codecs used and the compression rate.

Converting a 25Mbps AVCHD .mts file to a 25Mbps MPEG2 .mfx file will result in pretty much indistinguishable loss.

Converting a 384Kbps .wmv to a 384Kbps .mp4 will look lousier than oatmeal dumped into your DVD player.

As to a "copy of a copy", one of the most important aspects of preserving quality is to always start with as close to an original as possible. For example, if you have an original .mts file and you want to produce .mpg for DVD, .mp4 for youtube, and .wmv for your portable player, do *NOT* do this:

.mts -> .mpg, .mpg -> .mp4, .mp4 -> .wmv.

Instead, do it this way:

.mts -> .mpg
.mts -> .mp4
.mts -> .wmv