Since we're in the "Desktops" category, I assume we're talking about a system with a stationary location. Seems like a no-brainer to me: I would very much prefer to have a hardwired Ethernet connection to my desktop, which is quite some distance and one floor away from my home router. Such a connection would provide faster and much more reliable performance, free from interference from neighboring Wi-Fi networks (not to mention microwaves, wireless mice, etc.). The layout of our townhouse, however, makes installing such a line prohibitively difficult, so I make do with a high-powered USB-connected Wi-Fi adapter.
If given a choice, do you prefer running your system over wireless or ethernet for your network connection For more questions regarding this contest, please visit the Information Page here.
DS 07/25: You prefer to run your system, over wireless or ethernet network 
connection?