I just discovered the strange omission of Wine from the LMDE repositories...I'm sure there is some reasonable explanation for this, but in the meantime, some of us want to install Wine. It took some searching, but eventually I found this: http://crunchbanglinux.org/forums/post/129518/#p129518
A helpful fellow offers not only .debs of multiple Wine versions, but also a complete list of dependencies in case you want to build it yourself. Very convenient. They're compiled for Debian, but I'm guessing they will work fine for LMDE too. Haven't tested it much yet, but we'll see.